Question

find the derivative of $f(x)=x^{-5}$.

Explanation:

Step1: Apply the power rule

The power rule for differentiation is $\frac{d}{dx}(x^n)=nx^{n - 1}$. Here $n=-5$.

Step2: Calculate the derivative

Substitute $n = - 5$ into the power - rule formula. We get $f^\prime(x)=-5x^{-5 - 1}$.
Simplify the exponent: $f^\prime(x)=-5x^{-6}$.

Answer:

$f^\prime(x)=-\frac{5}{x^{6}}$