Differentiation Questions and Answers
Calculus
Differentiationy =
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
DifferentiationFind 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
DifferentiationConsider
y + In(xy) = 2
Determine the equation of the tangent line at (e, 1). Report the solution using slope-intercept form.
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) =
Calculus
DifferentiationLet 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.
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Calculus
DifferentiationLet g(x) = 5e7x - 6
Determine the derivative of g.
g'(x) =
Determine the slope of g at x = 4.
g'(4) =
Calculus
DifferentiationLet f(x)
Determine
=
- 7 cos( - 2x)
the derivative of f.
f'(x) =
Determine the slope of f at x = 7.
ƒ'(7) =
=
Calculus
DifferentiationUse the definition of derivative to find f'(x) and f(x).
f(x) = 5x² + 6x +3
f'(x) =
=
Calculus
DifferentiationFind 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
DifferentiationConsider
-4 ln(y) = 5y sin x
Determine the equation of the tangent line at (0, 1). Report the solution using slope-intercept form.
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Calculus
DifferentiationConsider
-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
DifferentiationLet 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
DifferentiationConsider
20
=
(tan(10y) +
Determine the derivative of y with respect to x.
dy
dx
csc (6x))8
Calculus
DifferentiationConsider
(sin(8x) + cot (4y))' = 5
Determine the derivative of y with respect to x.
y' =
Calculus
DifferentiationLet h(x) = (8x − 8)ª
Determine the derivative of h.
h'(x) =
Determine the slope of h at x = 1.
h’(1) =
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Calculus
DifferentiationConsider
x + 1
y 2
Determine the derivative of y with respect to x.
y'
= 34-7
Calculus
DifferentiationConsider
x² - y² = 18
-
Determine the derivative of y with respect to x.
y' =
-
Calculus
DifferentiationConsider
Determine the derivative of y with respect to x.
--
dy
dx
xy
=
x + 6
Y+4
- 3
-
Calculus
DifferentiationLet 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
DifferentiationConsider
tan(9x + 5y) = e9r
Determine the derivative of y with respect to x.
y'
Calculus
DifferentiationA 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
DifferentiationConsider
sec(3y) + sec(10x) = sec (3y)sec (10x)
Determine the derivative of y with respect to x.
dy
dx
Calculus
DifferentiationConsider
- 8 ln (x¹y³) - 5xy = − 5
Determine the derivative of y with respect to x.
y' =
Calculus
DifferentiationConsider
7-4=
Determine the derivative of y with respect to x.
dy
dx
||
x-1
y-8
Calculus
DifferentiationConsider
18
Determine the derivative of y with respect to x.
dy
dx
=
=
- 3x + y
x - 6y
Calculus
DifferentiationLet g(x)
Determine
g'(x) =
=
g'(1) =
- tan(- 9x)
the derivative of
g.
Determine the slope of g at x = 1.
Calculus
DifferentiationWrite the equation of the line tangent to the graph of y² = 6y + 6x + 22 at (-1, -2).
The equation is
Calculus
DifferentiationLet g(x) = ln (5x² - 20)
Determine
the derivative of g.
g'(x) =
Determine the slope of g at x = 7.
g'(7) =
Calculus
Differentiation1
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
DifferentiationConsider
2.8
7x²y³ = cot (8x²y³)
Determine the derivative of y with respect to x.
dy
dx
=
Calculus
DifferentiationLet h(x) = 4 tan² (8x)
Determine the derivative of h.
h'(x) =
Determine the slope of h at x = 9.
h'(9) =
Calculus
DifferentiationLet g(v) = ln(3v + 1)-6
Determine the derivative of g.
dg
dv
=
Determine the slope of g at v = - 8.
g'( − 8) =
Calculus
DifferentiationGiven
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
DifferentiationConsider
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
DifferentiationUse implicit differentiation to determine
dy
dx
dy
given the equation xy + sin(x) = tan(y).
dx
Calculus
DifferentiationConsider
8y¹ – 6 ln y - x6 = 11
Determine the derivative of y with respect to x.
dy
dx
Calculus
DifferentiationLet 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
DifferentiationConsider
− x¹ - xy + 6y5 = − 6
Determine the derivative of y with respect to x.
y' =