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(x) and g(x), then the derivative of their composition f(g(x)) is f'(g(x)) * g'(x).

Front

Differentiate: y = 2x^2(3x - 4)

Back

y' = 18x^2 - 16x

Front

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

Back

f'(x) = 30x^5(x^6 + 4)^4

Front

Differentiate: f(x) = x^7(5 + 8x)^3

Back

f'(x) = x^6(5 + 8x)^2(35 + 80x)

Front

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

Back

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

Front

Differentiate: f(x) = \frac{1}{x^2}

Back

f'(x) = -\frac{2}{x^3}

Front

What is the derivative of a constant function?

Back

The derivative of a constant function is zero.

Front

What is the power rule for differentiation?

Back

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

Front

What is the product rule for 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'.

Front

What is the quotient rule for differentiation?

Back

The quotient rule states that if u(x) and v(x) are functions, then the derivative of their quotient is (u'v - uv')/v^2.