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 y = cos^5(4x^3) using the Chain Rule.

Back

y' = -60x^2 cos^4(4x^3) sin(4x^3).

Front

Differentiate y = (csc(x) + 1)^7 using the Chain Rule.

Back

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

Front

Differentiate y = cos^5(x) using the Chain Rule.

Back

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

Front

Differentiate y = tan(3x^2 + 2) using the Chain Rule.

Back

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

Front

Differentiate y = ln(ln(2x)).

Back

y' = \frac{1}{x ln(2x)}.

Front

What is the derivative of a constant function?

Back

The derivative of a constant function is zero.

Front

What is the derivative of sin(x)?

Back

The derivative of sin(x) is cos(x).

Front

What is the derivative of cos(x)?

Back

The derivative of cos(x) is -sin(x).

Front

What is the derivative of tan(x)?

Back

The derivative of tan(x) is sec^2(x).