## anonymous 3 years ago differentiate the following equation sqrt(5)/(x^4)

1. abb0t

$$\frac{ \sqrt{5} }{ x^4 } = \sqrt{5} \frac{ d }{ dx }(x^{-4})$$ the $$\sqrt{5}$$ is a constant and can just be factored out.

2. anonymous

so would my final answer be 4x^3sqrt(5)

3. inkyvoyd

no... follow the power rule for differentiation: $$\frac{d}{dx}x^n=nx^{n-1}$$ remember that n=-4

4. anonymous

-4sqrt(5)/x^5

5. anonymous

oh ok can we leave the exponent as a negative

6. abb0t

yes.

7. abb0t

Or you can simplify it to make it look "nicer". Since you should recognize that: $$\huge a^{-n} = \frac{ 1 }{ a^n }$$

8. anonymous

Thanks