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**1. Homework Statement**

Prove by induction on k that for all integers

[tex] \frac{d}{dx} \prod_{i=1}^k f_i (x) = (\sum_{i=1}^k \frac{ \frac{d}{dx} f_i (x)}{f_i (x)} ) \prod_{i=1}^k f_i (x) [/tex]

**2. Homework Equations**

Product rule

[tex] \frac{d}{dx} (uv) = u \frac{dv}{dx} + v \frac{du}{dx} [/tex]

**3. The Attempt at a Solution**

I am honestly not sure how to start this. It is the first one like this that I have tried.