Chain Rule

Front

What is the Chain Rule in calculus?

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

Find y' for y = (2x + 1)^{10}.

Back

y' = 20(2x + 1)^{9}.

Front

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

Back

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

Front

Find the derivative of f(x) = (x^{6} + 4)^{5}.

Back

f'(x) = 30x^{5}(x^{6} + 4)^{4}.

Front

What is the derivative of a constant?

Back

The derivative of a constant is 0.

Front

If f(x) = g(h(x)), what is the derivative f'(x) using the Chain Rule?

Back

f'(x) = g'(h(x)) * h'(x).

Front

What is the derivative of f(x) = (3x + 2)^{4}?

Back

f'(x) = 36(3x + 2)^{3}.

Front

How do you apply the Chain Rule to find the derivative of f(x) = sin(g(x))?

Back

f'(x) = cos(g(x)) * g'(x).

Front

What is the derivative of f(x) = e^{g(x)}?

Back

f'(x) = e^{g(x)} * g'(x).

Front

Find the derivative of f(x) = (x^{2} + 1)^{3}.

Back

f'(x) = 6x(x^{2} + 1)^{2}.