Chain Rule Practice

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 f(g(x)), the derivative is f'(g(x)) * g'(x).

Front

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

Back

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

Front

When do you use the Chain Rule?

Back

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

Front

What is a derivative?

Back

A derivative represents the rate of change of a function with respect to a variable.

Front

What is another way to describe a derivative?

Back

Slope of the tangent line.

Front

Find the derivative of p = 1/√(q + 9).

Back

dp/dq = -1/(2(q + 9)^(3/2)).

Front

What is the derivative of f(g(x))?

Back

f '(g(x))g'(x).

Front

What does f '(x) represent?

Back

f '(x) represents the derivative of the function f with respect to x.

Front

If f(x) = x^2, what is f '(x)?

Back

f '(x) = 2x.

Front

What is the power rule for derivatives?

Back

If f(x) = x^n, then f '(x) = nx^(n-1).