Differentiation Questions and Answers

What is the modulus of the conjugate of (2 + 3)?
O √13
O √15
O√5
O√3
Calculus
Differentiation
What is the modulus of the conjugate of (2 + 3)? O √13 O √15 O√5 O√3
y =
Find
dy
dx
(9x + cot(x))7
dy
dx
||
Type sin(x) for sin(x), cos(x) for cos(x), and so on.
Use x^2 to square x, x^3 to cube x, and so on.
Use (sin(x))^2 to square sin(x).
Calculus
Differentiation
y = Find dy dx (9x + cot(x))7 dy dx || Type sin(x) for sin(x), cos(x) for cos(x), and so on. Use x^2 to square x, x^3 to cube x, and so on. Use (sin(x))^2 to square sin(x).
Find dy/dx by implicit differentiation.
(сos лx + sin лу)³ = 13
dy/dx =
Calculus
Differentiation
Find dy/dx by implicit differentiation. (сos лx + sin лу)³ = 13 dy/dx =
Find the derivative of f(x) = f(x) = 7√x - √
3
x
10
3
10
T
Type your answer without fractional or negative exponents. Use sqrt(x) for √√√.
f(x) = f'(x) =
Calculus
Differentiation
Find the derivative of f(x) = f(x) = 7√x - √ 3 x 10 3 10 T Type your answer without fractional or negative exponents. Use sqrt(x) for √√√. f(x) = f'(x) =
Solve csc (5x) - 7 = 0 for the four smallest positive solutions
C =
Calculus
Differentiation
Solve csc (5x) - 7 = 0 for the four smallest positive solutions C =
Consider
y + In(xy) = 2
Determine the equation of the tangent line at (e, 1). Report the solution using slope-intercept form.
Calculus
Differentiation
Consider y + In(xy) = 2 Determine the equation of the tangent line at (e, 1). Report the solution using slope-intercept form.
(1) If f(x) = x, then f'(x) =
(2) If g(x) =
(3) If h(x) =
- 5x4, then g'(x) =
1
x5'
then h'(x) =
Calculus
Differentiation
(1) If f(x) = x, then f'(x) = (2) If g(x) = (3) If h(x) = - 5x4, then g'(x) = 1 x5' then h'(x) =
Let h(w) = -6 sin³ (2πw)
Determine the value(s) of w on (0, 1), if any, for which h has a horizontal tangent line. If mulitple such values
of w exist, use a comma-separated list to enter the solutions.
Oh has a horizontal tangent line at w =
h has no horizontal tangent lines.
Submit Question
Calculus
Differentiation
Let h(w) = -6 sin³ (2πw) Determine the value(s) of w on (0, 1), if any, for which h has a horizontal tangent line. If mulitple such values of w exist, use a comma-separated list to enter the solutions. Oh has a horizontal tangent line at w = h has no horizontal tangent lines. Submit Question
Let g(x) = 5e7x - 6
Determine the derivative of g.
g'(x) =
Determine the slope of g at x = 4.
g'(4) =
Calculus
Differentiation
Let g(x) = 5e7x - 6 Determine the derivative of g. g'(x) = Determine the slope of g at x = 4. g'(4) =
Let f(x)
Determine
=
- 7 cos( - 2x)
the derivative of f.
f'(x) =
Determine the slope of f at x = 7.
ƒ'(7) =
=
Calculus
Differentiation
Let f(x) Determine = - 7 cos( - 2x) the derivative of f. f'(x) = Determine the slope of f at x = 7. ƒ'(7) = =
Use the definition of derivative to find f'(x) and f(x).
f(x) = 5x² + 6x +3
f'(x) =
=
Calculus
Differentiation
Use the definition of derivative to find f'(x) and f(x). f(x) = 5x² + 6x +3 f'(x) = =
Find dy/dx by implicit differentiation.
(4x + 4y)³ = 64x³ + 64y³,
dy
dx
=
At (-1, 1): y' =
Then find the slope of the graph at the given point.
(-1, 1)
Calculus
Differentiation
Find dy/dx by implicit differentiation. (4x + 4y)³ = 64x³ + 64y³, dy dx = At (-1, 1): y' = Then find the slope of the graph at the given point. (-1, 1)
Let h(y) = ln (y(y³ + 1) ¹)
Determine the derivative of h.
dh
dy
Calculus
Differentiation
Let h(y) = ln (y(y³ + 1) ¹) Determine the derivative of h. dh dy
Consider
-4 ln(y) = 5y sin x
Determine the equation of the tangent line at (0, 1). Report the solution using slope-intercept form.
Submit Question
Calculus
Differentiation
Consider -4 ln(y) = 5y sin x Determine the equation of the tangent line at (0, 1). Report the solution using slope-intercept form. Submit Question
Find
dy
dx
dy
dx
where
y²e-5x – 9x² - y² = 8
-
Calculus
Differentiation
Find dy dx dy dx where y²e-5x – 9x² - y² = 8 -
Consider
-9x5 +7x³6y + y² = − 1
Determine the derivative of y with respect to x.
y'
Determine the equation of the tangent line to the curve at (1, 1). Report the solution usine slope-intercept
form.
Calculus
Differentiation
Consider -9x5 +7x³6y + y² = − 1 Determine the derivative of y with respect to x. y' Determine the equation of the tangent line to the curve at (1, 1). Report the solution usine slope-intercept form.
Let f(y)
=
35
(y - 3)²
Determine the value(s) of y, if any, for which f has a horizontal tangent line. If mulitple such values of y
exist, use a comma-separated list to enter the solutions.
of has a horizontal tangent line at y =
Of has no horizontal tangent lines.
Calculus
Differentiation
Let f(y) = 35 (y - 3)² Determine the value(s) of y, if any, for which f has a horizontal tangent line. If mulitple such values of y exist, use a comma-separated list to enter the solutions. of has a horizontal tangent line at y = Of has no horizontal tangent lines.
Consider
20
=
(tan(10y) +
Determine the derivative of y with respect to x.
dy
dx
csc (6x))8
Calculus
Differentiation
Consider 20 = (tan(10y) + Determine the derivative of y with respect to x. dy dx csc (6x))8
Consider
(sin(8x) + cot (4y))' = 5
Determine the derivative of y with respect to x.
y' =
Calculus
Differentiation
Consider (sin(8x) + cot (4y))' = 5 Determine the derivative of y with respect to x. y' =
Let h(x) = (8x − 8)ª
Determine the derivative of h.
h'(x) =
Determine the slope of h at x = 1.
h’(1) =
Submit All Parts
Calculus
Differentiation
Let h(x) = (8x − 8)ª Determine the derivative of h. h'(x) = Determine the slope of h at x = 1. h’(1) = Submit All Parts
Consider
x + 1
y 2
Determine the derivative of y with respect to x.
y'
= 34-7
Calculus
Differentiation
Consider x + 1 y 2 Determine the derivative of y with respect to x. y' = 34-7
Find the first derivative with respect to x.
- 2x² - 9y² + 7y = 8
dy
dx
=
Calculus
Differentiation
Find the first derivative with respect to x. - 2x² - 9y² + 7y = 8 dy dx =
Consider
x² - y² = 18
-
Determine the derivative of y with respect to x.
y' =
-
Calculus
Differentiation
Consider x² - y² = 18 - Determine the derivative of y with respect to x. y' = -
Consider
Determine the derivative of y with respect to x.
--
dy
dx
xy
=
x + 6
Y+4
- 3
-
Calculus
Differentiation
Consider Determine the derivative of y with respect to x. -- dy dx xy = x + 6 Y+4 - 3 -
Let f(x) = x(3x)²
Determine the equation of the tangent line to f at (5, 20). Report the solution using slope-intercept form.
Calculus
Differentiation
Let f(x) = x(3x)² Determine the equation of the tangent line to f at (5, 20). Report the solution using slope-intercept form.
Consider
tan(9x + 5y) = e9r
Determine the derivative of y with respect to x.
y'
Calculus
Differentiation
Consider tan(9x + 5y) = e9r Determine the derivative of y with respect to x. y'
6x
√√²+1
Determine the derivative of g.
Let g(x)
g'(x) =
=
Calculus
Differentiation
6x √√²+1 Determine the derivative of g. Let g(x) g'(x) = =
-7x + 7
x² + 6
Determine the derivative of h
Let h(x) =
h'(x) =
5
=
+7)
Calculus
Differentiation
-7x + 7 x² + 6 Determine the derivative of h Let h(x) = h'(x) = 5 = +7)
A plane flies 452 miles north and
then 767 miles west.
What is the magnitude of the
plane's resultant vector?
Hint: Draw a vector diagram.
[?] miles
Calculus
Differentiation
A plane flies 452 miles north and then 767 miles west. What is the magnitude of the plane's resultant vector? Hint: Draw a vector diagram. [?] miles
Find the first derivative with respect to x.
− 13x7 + 1ly7 + 2y = 15
dy
dx
Calculus
Differentiation
Find the first derivative with respect to x. − 13x7 + 1ly7 + 2y = 15 dy dx
Consider
sec(3y) + sec(10x) = sec (3y)sec (10x)
Determine the derivative of y with respect to x.
dy
dx
Calculus
Differentiation
Consider sec(3y) + sec(10x) = sec (3y)sec (10x) Determine the derivative of y with respect to x. dy dx
Consider
- 8 ln (x¹y³) - 5xy = − 5
Determine the derivative of y with respect to x.
y' =
Calculus
Differentiation
Consider - 8 ln (x¹y³) - 5xy = − 5 Determine the derivative of y with respect to x. y' =
Consider
7-4=
Determine the derivative of y with respect to x.
dy
dx
||
x-1
y-8
Calculus
Differentiation
Consider 7-4= Determine the derivative of y with respect to x. dy dx || x-1 y-8
Consider
18
Determine the derivative of y with respect to x.
dy
dx
=
=
- 3x + y
x - 6y
Calculus
Differentiation
Consider 18 Determine the derivative of y with respect to x. dy dx = = - 3x + y x - 6y
Let h(z) = In
Determine
h'(z) =
√7z+8
the derivative of h.
Calculus
Differentiation
Let h(z) = In Determine h'(z) = √7z+8 the derivative of h.
Let g(x)
Determine
g'(x) =
=
g'(1) =
- tan(- 9x)
the derivative of
g.
Determine the slope of g at x = 1.
Calculus
Differentiation
Let g(x) Determine g'(x) = = g'(1) = - tan(- 9x) the derivative of g. Determine the slope of g at x = 1.
Write the equation of the line tangent to the graph of y² = 6y + 6x + 22 at (-1, -2).
The equation is
Calculus
Differentiation
Write the equation of the line tangent to the graph of y² = 6y + 6x + 22 at (-1, -2). The equation is
Let g(x) = ln (5x² - 20)
Determine
the derivative of g.
g'(x) =
Determine the slope of g at x = 7.
g'(7) =
Calculus
Differentiation
Let g(x) = ln (5x² - 20) Determine the derivative of g. g'(x) = Determine the slope of g at x = 7. g'(7) =
1
4x² - 9 + 9x
Use the chain rule to determine the derivative of f.
Let f(x)
=
f'(x) =
Determine the slope of f at x = 2.
f'(2) =
CAR
Calculus
Differentiation
1 4x² - 9 + 9x Use the chain rule to determine the derivative of f. Let f(x) = f'(x) = Determine the slope of f at x = 2. f'(2) = CAR
Consider
2.8
7x²y³ = cot (8x²y³)
Determine the derivative of y with respect to x.
dy
dx
=
Calculus
Differentiation
Consider 2.8 7x²y³ = cot (8x²y³) Determine the derivative of y with respect to x. dy dx =
Let h(x) = 4 tan² (8x)
Determine the derivative of h.
h'(x) =
Determine the slope of h at x = 9.
h'(9) =
Calculus
Differentiation
Let h(x) = 4 tan² (8x) Determine the derivative of h. h'(x) = Determine the slope of h at x = 9. h'(9) =
Let g(v) = ln(3v + 1)-6
Determine the derivative of g.
dg
dv
=
Determine the slope of g at v = - 8.
g'( − 8) =
Calculus
Differentiation
Let g(v) = ln(3v + 1)-6 Determine the derivative of g. dg dv = Determine the slope of g at v = - 8. g'( − 8) =
Use this definition to find f'(a) at the given number a.
f(x) =
5x+1 a = 3
Calculus
Differentiation
Use this definition to find f'(a) at the given number a. f(x) = 5x+1 a = 3
;)
Determine the derivative of g.
Let g(t) = In
dg
dt
8t
=
t - 12
Calculus
Differentiation
;) Determine the derivative of g. Let g(t) = In dg dt 8t = t - 12
Given
h(x) = g(f(x))
• At x = 0, the equation of the tangent line of g is y = 3x - 1.
• At x = 5, the equation of the tangent line of fis y = -9x + 45.
Determine h'(5)
h'(5)=
•
Calculus
Differentiation
Given h(x) = g(f(x)) • At x = 0, the equation of the tangent line of g is y = 3x - 1. • At x = 5, the equation of the tangent line of fis y = -9x + 45. Determine h'(5) h'(5)= •
Consider
26x7 + 3x65y + y¹0 = 30
10
Determine the derivative of y with respect to x.
dy
dx
Determine the equation of the tangent line to the curve at (1, 1). Report the solution usine slope-intercept
form.
Calculus
Differentiation
Consider 26x7 + 3x65y + y¹0 = 30 10 Determine the derivative of y with respect to x. dy dx Determine the equation of the tangent line to the curve at (1, 1). Report the solution usine slope-intercept form.
Use implicit differentiation to determine
dy
dx
dy
given the equation xy + sin(x) = tan(y).
dx
Calculus
Differentiation
Use implicit differentiation to determine dy dx dy given the equation xy + sin(x) = tan(y). dx
Consider
8y¹ – 6 ln y - x6 = 11
Determine the derivative of y with respect to x.
dy
dx
Calculus
Differentiation
Consider 8y¹ – 6 ln y - x6 = 11 Determine the derivative of y with respect to x. dy dx
Let h(y) In(7y - 1)
Determine the derivative of h.
h'(y)
=
Determine the interval(s) on which h is differentiable. Report the solution using invterval notation.
h is differentiable on
Calculus
Differentiation
Let h(y) In(7y - 1) Determine the derivative of h. h'(y) = Determine the interval(s) on which h is differentiable. Report the solution using invterval notation. h is differentiable on
Consider
− x¹ - xy + 6y5 = − 6
Determine the derivative of y with respect to x.
y' =
Calculus
Differentiation
Consider − x¹ - xy + 6y5 = − 6 Determine the derivative of y with respect to x. y' =