Chain Rule Implicit Differentiation Inverse Functions

Differentiate the function y = cos^-1(x) with respect to x. dy/dx =

Mathematical Equivalence

ON

Use implicit differentiation to find dy/dx for the equation x²y + xy² = 10.

Mathematical Equivalence

ON

Find the derivative of the inverse function y = f^-1(x) if f(x) = 3x³ + 2.

Differentiate the function y = sec^-1(x) with respect to x.

The graph of f(x) is given. If h(x) = (f(x))³, what is the instantaneous rate of change of h(x) at x = 2?

• 1/2

• 1

• 3/2

• 3

Find the second derivative of the following functions with respect to x.
y=(3x+2)¹⁰ d²y/dx² =

Mathematical Equivalence

ON

The function f is given by f(x) = 2ln(1 - x²) + e^x, where f(0) = 1. If h(x) = -3f^-1(x), what is h'(1)?

• -1/3

• -3

• 0

• 1

Apply the chain rule to find the derivative of y = (2x + 1)⁴.

Find the derivative of the inverse function y = f^-1(x) if f(x) = x² - 4 (for x ≥ 0).