find the derivative of $f(x)=x^{-5}$.
find the derivative of $f(x)=x^{-5}$.
Answer
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:
$f^\prime(x)=-\frac{5}{x^{6}}$