Chain Rule Differentiation

Front

What is the Chain Rule in differentiation?

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

Differentiate f(x) = 7(3x + 4)^5

Back

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

Front

Differentiate f(x) = (x^3 - 2x)^2

Back

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

Front

Differentiate f(x) = (x^2 + 1)^6

Back

f'(x) = 12x(x^2 + 1)^5.

Front

Differentiate y = (2x + 1)^10

Back

y' = 20(2x + 1)^9.

Front

Differentiate f(x) = (9 - 4x^2)^-1

Back

f'(x) = 8x/(9 - 4x^2)^2.

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 find the derivative of f(x) = sin(3x + 2)?

Back

f'(x) = cos(3x + 2) * 3.

Front

What is the product rule in differentiation?

Back

The product rule states that if u(x) and v(x) are functions, then the derivative of their product is u'v + uv'.