1. ## Radical derivative problem, dude

I need to find the derivative of $\displaystyle f(x) = 5e^x * x^{\frac{1}{6}}$

So far I've gotten $\displaystyle 5e^x * \frac{1}{6} * x^{\frac{-5}{6}}$
However, I'm uncertain where to go next.
I thought $\displaystyle x^{\frac{-5}{6}} = \frac{1}{x^{\frac{5}{6}}}$
Ergo I would end up with $\displaystyle \frac{5e^x}{6x^{5/6}}$

That's obviously wrong, though...

2. ## Re: Radical derivative problem, dude

Originally Posted by Nervous
I need to find the derivative of $\displaystyle f(x) = 5e^x * x^{\frac{1}{6}}$

So far I've gotten $\displaystyle 5e^x * \frac{1}{6} * x^{\frac{-5}{6}}$
However, I'm uncertain where to go next.
I thought $\displaystyle x^{\frac{-5}{6}} = \frac{1}{x^{\frac{5}{6}}}$
Ergo I would end up with $\displaystyle \frac{5e^x}{6x^{5/6}}$

That's obviously wrong, though...
You have a product, so you need to use the Product Rule.

\displaystyle \displaystyle \begin{align*} \frac{d}{dx}\left[f(x)\,g(x)\right] &= f(x)\,\frac{d\,g(x)}{dx} + g(x)\,\frac{d\,f(x)}{dx} \end{align*}