Calculus Derivative using Chain Rule Basic

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}.

Tags

CCSS.HSA.APR.C.5

Front

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

Back

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

Front

Find the derivative of f(x) = 7(3x + 4)^{5}.

Back

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

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 power rule for derivatives?

Back

The power rule states that if f(x) = x^n, then f'(x) = n*x^{n-1}.

Front

How do you differentiate a function raised to a power?

Back

Use the Chain Rule: if y = (u(x))^n, then y' = n*(u(x))^{n-1} * u'(x).

Front

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

Back

f'(x) = n*x^{n-1}.