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

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

Back

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

Front

Differentiate f(x) = (x^6 + 4)^5

Back

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

Front

Differentiate y = (2x + 1)^{10}

Back

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

Front

What is the derivative of a constant?

Back

The derivative of a constant is 0.

Front

If f(x) = g(x)h(x), what is the product rule?

Back

The product rule states that (fg)' = f'g + fg'.

Front

If f(x) = g(h(x)), what is the formula for the Chain Rule?

Back

The Chain Rule states that f'(x) = g'(h(x)) * h'(x).

Front

What is the derivative of f(x) = sin(x^2)?

Back

f'(x) = 2x cos(x^2) using the Chain Rule.

Front

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

Back

f'(x) = e^{g(x)} * g'(x) using the Chain Rule.

Front

Differentiate f(x) = ln(g(x)).

Back

f'(x) = g'(x)/g(x) using the Chain Rule.