Question

homework4: problem 14 (1 point) differentiate the following function: $g(x)=x^{5}+\frac{1}{x^{5}}$ $g(x)=$ you have attempted this problem 0 times. you have unlimited attempts remaining. email instructor

Explanation:

Step1: Rewrite the function

Rewrite $g(x)=x^{5}+\frac{1}{x^{5}}$ as $g(x)=x^{5}+x^{- 5}$.

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 $5x^{5 - 1}=5x^{4}$.
For the second term $x^{-5}$, its derivative is $-5x^{-5 - 1}=-5x^{-6}=-\frac{5}{x^{6}}$.

Step3: Find the derivative of the function

$g^\prime(x)$ is the sum of the derivatives of the two terms. So $g^\prime(x)=5x^{4}-\frac{5}{x^{6}}$.

Answer:

$5x^{4}-\frac{5}{x^{6}}$