Calculus 10th Edition

Rewrite: $\frac{3}{2}x^{-4}$; Differentiate: $(\frac{3}{2})(-4)(x^{-4-1})$; Simplify: $\frac{-6}{x^5}$ .
To rewrite, use the index rule $\frac{1}{x^n}$ is equal to $x^{-n}$; hence, the function becomes $(\frac{3}{2})(x^{-4})$. To differentiate, use the power rule to find the derivative of $x^{-4}$ which is $(-4)(x^{-4-1})$; hence, the derivative of the overall function is just the derivative of $x^{-4}$ times the constant $\frac{3}{2}$. To simplify, both the numerator and denominator can be simplified by two leaving a $-6$; furthermore, $x^{-5}$ can be taken to the denominator; hence, the overall simplified derivative is $\frac{-6}{x^5}$.