Chain Rule Review

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).

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

$$f'(x) = 3x^2 + 2x$$

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

$$f'(x) = \frac{8x}{(9 - 4x^2)^{2}}$$

$$f'(x) = 6x^{5} - 16x^{3} + 8x$$

The derivative of a constant function is zero.

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

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

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.