Question

find $f(x)$ if $f(x)=x^{-5}+\frac{1}{x^{9}}$. answer: submit answer next item

Explanation:

Step1: Rewrite the function

Rewrite $\frac{1}{x^{9}}$ as $x^{-9}$, so $f(x)=x^{-5}+x^{-9}$.

Step2: Apply power - rule for differentiation

The power - rule states that if $y = x^{n}$, then $y^\prime=nx^{n - 1}$.
For the first term $x^{-5}$, its derivative is $-5x^{-5 - 1}=-5x^{-6}$.
For the second term $x^{-9}$, its derivative is $-9x^{-9 - 1}=-9x^{-10}$.

Step3: Find the derivative of the function

$f^\prime(x)=-5x^{-6}-9x^{-10}$.

Answer:

$-5x^{-6}-9x^{-10}$