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

Front

Differentiate: y = sin(2x^2)

Back

y' = 4x cos(2x^2) using the Chain Rule.

Front

Differentiate: y = cos^3(x)

Back

y' = -3 sin(x) cos^2(x) using the Chain Rule.

Front

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

Back

f'(x) = 30x^5 (x^6 + 4)^4 using the Chain Rule.

Front

Differentiate: f(x) = (6x^2 - 5x)^7

Back

f'(x) = 7(6x^2 - 5x)^6 (12x - 5) using the Chain Rule.

Front

Differentiate: f(t) = (t^2 + 2t)^5

Back

f'(t) = 5(t^2 + 2t)^4 (2t + 2) using the Chain Rule.

Front

What is the derivative of a constant function?

Back

The derivative of a constant function is zero.

Front

What is the power rule in differentiation?

Back

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

Front

How do you apply the Chain Rule to composite functions?

Back

To apply the Chain Rule, differentiate the outer function and multiply it by the derivative of the inner function.

Front

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

Back

The derivative is e^(g(x)) * g'(x) using the Chain Rule.