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) = (6x^2 - 5x)^7.

Back

f'(x) = 7(6x^2 - 5x)^6 * (12x - 5).

Front

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

Back

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

Front

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

Back

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

Front

Differentiate y = (2x + 1)^{10}.

Back

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

Front

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

Back

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

Front

What is the derivative of a constant function?

Back

The derivative of a constant function is 0.

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 product rule in differentiation?

Back

If u(x) and v(x) are functions, then the derivative of their product is u'v + uv'.

Front

How do you apply the quotient rule in differentiation?

Back

If u(x) and v(x) are functions, then the derivative of their quotient is (u'v - uv')/v^2.