Warm up (10/24/19)

The formula for the volume of a cone is $$V = \frac{1}{3} \pi r^2 h$$ , where r is the radius of the base and h is the height.

The product rule states that if you have two functions u(x) and v(x), the derivative of their product is given by: $$(uv)' = u'v + uv'$$ .

You can rewrite it as $$(x^2 - 1)^{2}$$ to apply the chain rule.

The chain rule states that if you have a composite function f(g(x)), the derivative is given by: $$f'(g(x))g'(x)$$ .

The derivative is $$-\frac{1}{4}(x^2 - 1)^{-\frac{3}{2}} \times 2x = -\frac{x}{2(x^2 - 1)^{\frac{3}{2}}}$$ .

The formula for the area of a circle is $$A = \pi r^2$$ , where r is the radius.

A function is a specific type of relation where each input has exactly one output.

A limit is the value that a function approaches as the input approaches a certain value.

The derivative of $$x^3$$ is $$3x^2$$ .

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