# Derivative rules: Products and quotients

Find the following derivatives. Indicate which derivative rules are being used.

1. Let $$y = x^2 \cdot \ln{x}$$. What is $$\frac{dy}{dx}$$? (Recall that $$\frac{d}{dx} \ln{x} = \frac{1}{x}$$.)

2. Suppose $$g(x) = \dfrac{x^2}{x^9+1}$$. What is the derivative of $$g(x)$$ with respect to $$x$$?

## Challenge

3. Find $$\frac{d}{dx} (x^2 \cdot \ln{x} \cdot e^x)$$.

4. Let $$h(x) = 2x^3 \cdot \ln{x}$$. What is $$h''(x)$$?