Differentiation Questions and Answers

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).

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) =

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.

(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

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) = =

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)

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

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.

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

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

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 =

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 -

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'

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)

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

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' =

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

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.

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) =

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 =

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) =

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

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.

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

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' =