## Calculus 10th Edition

Rewrite:$(\frac{6}{125})(x^{-3})$; Differentiate: $(\frac{6}{125})(-3)(x^{-3-1})$; Simplify: $\frac{-18}{125x^4}$
To simplify, you have to make sure to notice that not only $x$ is raised to to the power of $3$, it is $5x$ that is raised; hence the denominator becomes $125x^{3}$. Then, you have to take $x^{3}$ to the numerator by flipping the sign of the power; hence we get :$(\frac{6}{125})(x^{-3})$. To differentiate, just use the power rule to find the derivative of $x^{-3}$ which is $(-3)(x^{-3-1})$. The overall derivative is the derivative of $x^{-3}$ times the constant $\frac{6}{125}$. Hence we get $(\frac{6}{125})(-3)(x^{-3-1})$. To simplify, you have to take the $x^{-4}$ to the denominator and flipping the exponent's sign (Index rule: $x^{-n}=\frac{1}{x^n}$ ). Hence the overall final derivative is $\frac{-18}{125x^4}$.