Section 3.4

Find the derivative. y = (x^-2 + x)^-3

dy/dx = 3x^5(2-x^3)/(1+x^3)^4

Find the derivative. Find f '(x) for f(x) = (4x^2 + 3x)^2.

f'(x) = 64x^3 + 72x^2 + 18x

Provide an appropriate response. Find f '(x) for f(x) = (4x^2 + 3x)^2.

f'(x) = 64x^3 + 72x^2 + 18x

Provide an appropriate response. Consider the function: f(x) = 1/√11-x^2. Choose the answer choice that includes all of the pair(s) of functions from the list so that f(x) can be written as a composition: f(x) = g(h(x)).

g(x) = 1/√11-x; h(x) = x^2

Find all values of x for the given function where the tangent line is horizontal. f(x) = x/(x^2+1)^3

±√5/5

Provide an appropriate response. Find the composition f[g(x)] if f(u) = u^5 and g(x) = 2 - 3x^2.

(2 - 3x^2)^5

Find the derivative. Find f '(x) for f(x) = (8x - 9)^-4.

- 32/(8x-9)^5

Find the derivative. Find d/dw 4/(w^2+3)^5

-40w/(w^2+3)^6

Provide an appropriate response. Find dy/dt for y = (5t^2 - 4t)^2.

2(5t^2 - 4t)(10t-4)

Provide an appropriate response. Find the composite g[f(-k)] if f(x) = 8x^2 - 5x and g(x) = 7x + 9.

56k^2 + 35k + 9

Find the derivative. Find: d/dx [8√8x^7-10]

7x^6/(8x^7-10)^7/8

Provide an appropriate response. Find dy/dx for y = ln (3x^3 - x^2)

9x-2/3x^2-x

Provide an appropriate response. Consider the function: f(x) = √9-x^2/x^2. Choose the answer choice that includes all of the pair(s) of functions from the list so that f(x) can be written as a composition: f(x) = g(h(x)).

Both A and B

Provide an appropriate response. Write composite function y = (2x^4 + 3x + 1)^3 in the form y = f(u) and u = g(x).

IDK yet