Unsure how to find part of derivative

Question

$$\frac{5}{6x^5}+\tan(\frac{\pi}{9})$$

I'm reviewing questions and the derivative is supposed to be $$\frac{-25}{6}x^{-6}$$

But I can't remember how I got the $-\frac{25}{6}$. The rest I've got but not that.

Answer 1

We start with $$\frac{5}{6x^5}+\tan(\pi/9)$$ Then we take derivative $$\frac{d}{dx}\bigg[\frac{5}{6x^5}+\tan(\pi/9)\bigg]$$ $$\frac{d}{dx}\frac{5}{6x^5}+\frac{d}{dx}\tan(\pi/9)$$ $$\frac{5}{6}\frac{d}{dx}x^{-5}$$ $$\frac{5}{6}(-5x^{-6})$$ $$\frac{-25}{6}x^{-6}$$

Answer 2

For starters, $\tan(\frac{\pi}{9})$ is a constant, so won't show up in your final solution. (The derivative of a constant is $0$.).

That leaves you with $$\frac{5}{6x^5}$$

Rewrite it and use the power rule.

$$\frac{d}{dx}\frac{5}{6}x^{-5}= -\frac{5\times 5}{6}x^{-6}=-\frac{25}{6x^6}$$