AP Calculus AB Review #2

$$f'(x) = -\frac{1}{x^2}$$

The average value is given by $$\frac{1}{b-a} \times \text{integral from } a \text{ to } b f(x)dx$$ .

If $$f(x) = u(x)v(x)$$ , then $$f'(x) = u'(x)v(x) + u(x)v'(x)$$ .

If $$f(g(x))$$ , then $$f'(g(x)) \times g'(x)$$ .

$$\text{The integral is } \text{ln}|x| + C$$ .

It states that if $$F$$ is an antiderivative of $$f$$ on an interval [a, b], then $$\text{integral from } a \text{ to } b f(x)dx = F(b) - F(a)$$ .

A function defined by different expressions for different intervals of the domain.

Evaluate the function at that value or use algebraic manipulation to simplify.

$$f'(x) = 2x \text{cos}(2x) - 2x^2 \text{sin}(2x)$$ .

$$\text{The integral is } \text{asin}(x) + C$$ .