AP Calculus Midterm Review

The derivative is $$-\frac{x^2}{y^2}$$ .

The function is decreasing.

The derivative is defined as $$\lim_{h\rightarrow0}\ \frac{f\left(x+h\right)-f\left(x\right)}{h}$$ .

The slope is 12.

The IVT is primarily concerned with y-values.

If $$f(x) = x^n$$ , then $$f'(x) = nx^{n-1}$$ .

If $$y = f(g(x))$$ , then $$\frac{dy}{dx} = f'(g(x)) \cdot g'(x)$$ .

If $$u(x)$$ and $$v(x)$$ are functions, then $$\frac{d}{dx}[u(x)v(x)] = u'(x)v(x) + u(x)v'(x)$$ .

If $$u(x)$$ and $$v(x)$$ are functions, then $$\frac{d}{dx}\left[\frac{u(x)}{v(x)}\right] = \frac{u'v - uv'}{v^2}$$ .

It states that if $$F$$ is an antiderivative of $$f$$ on an interval [a, b], then $$\int_a^b f(x)dx = F(b) - F(a)$$ .