DERIVATIVE 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' is given by y' = f'(g(x)) * g'(x).

Front

Differentiate the function y = cos(4x^3).

Back

y' = -12x^2sin(4x^3).

Front

Differentiate the function y = sin(x^3 - 2x).

Back

y' = (3x^2 - 2)cos(x^3 - 2x).

Front

What is the derivative of y = cos^5(x)?

Back

y' = -5cos^4(x)sin(x).

Front

Differentiate the function y = (csc(x) + 1)^7.

Back

y' = -7(csc(x) + 1)^6(csc(x)cot(x)).

Front

Differentiate the function y = tan(3x^2 + 2).

Back

y' = 6xsec^2(3x^2 + 2).

Front

What is the formula for the derivative of sin(u) where u is a function of x?

Back

If y = sin(u), then y' = cos(u) * u', where u' is the derivative of u with respect to x.

Front

What is the formula for the derivative of cos(u) where u is a function of x?

Back

If y = cos(u), then y' = -sin(u) * u', where u' is the derivative of u with respect to x.

Front

What is the derivative of y = e^(g(x))?

Back

y' = e^(g(x)) * g'(x).

Front

What is the derivative of y = ln(g(x))?

Back

y' = (1/g(x)) * g'(x).