Derivatives Review: Power, Product, and Quotient Rules

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

The Product Rule states that if $$h(x) = f(x) * g(x)$$ , then $$h'(x) = f'(x) * g(x) + f(x) * g'(x)$$ .

The Quotient Rule states that if $$h(x) = \frac{f(x)}{g(x)}$$ , then $$h'(x) = \frac{f'(x) * g(x) - f(x) * g'(x)}{(g(x))^2}$$ .

To find the slope of the tangent line at a point $$x=a$$ , compute $$f'(a)$$ .

The equation is given by $$y - f(a) = f'(a)(x - a)$$ .

The slope of the normal line is the negative reciprocal of the slope of the tangent line.

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

$$f'(x) = 12x^2$$ .

$$h(x) = x^5$$ .

$$h'(x) = f'(x) + g'(x)$$ .