Chain Rule Differentiation

Front

What is the Chain Rule in differentiation?

Back

The Chain Rule is a formula for computing the derivative of the composition of two or more functions. It states that if you have a function y = f(g(x)), then the derivative y' = f'(g(x)) * g'(x).

Front

When do you use the Chain Rule?

Back

You use the Chain Rule when there is a function within another function.

Front

Differentiate f(x) = (9 - 4x^2)^-1

Back

f'(x) = 8x/(9 - 4x^2)^2.

Front

Find the derivative of f(x) = (x^3 - 2x)^2

Back

f'(x) = 6x^5 - 16x^3 + 8x.

Front

Differentiate f(x) = (x^2 + 1)^6

Back

f'(x) = 12x(x^2 + 1)^5.

Front

Differentiate f(x) = 7(3x + 4)^5

Back

f'(x) = 105(3x + 4)^4.

Front

What is the first step in applying the Chain Rule?

Back

Identify the outer function and the inner function in the composition.

Front

How do you find the derivative of a composite function?

Back

Differentiate the outer function, then multiply by the derivative of the inner function.

Front

What is an example of a function that requires the Chain Rule?

Back

f(x) = sin(3x^2 + 1) requires the Chain Rule because it is a composition of sine and a polynomial.

Front

Differentiate f(x) = e^(2x^3)

Back

f'(x) = 6x^2 * e^(2x^3).