question find the derivative of f(x)= -\\frac{1}{x^{7}}+x + 4. provide your answer below: f(x)=□

Explanation:

Step1: Rewrite the function

Rewrite $f(x)=-\frac{1}{x^{7}}+x + 4$ as $f(x)=-x^{-7}+x + 4$.

Step2: Apply power - rule for derivatives

The power - rule states that if $y = x^{n}$, then $y^\prime=nx^{n - 1}$. For $y=-x^{-7}$, $y^\prime=-(-7)x^{-7 - 1}=7x^{-8}$. For $y = x$, $y^\prime=1x^{1 - 1}=1$. For $y = 4$, since the derivative of a constant is 0, $y^\prime = 0$.

Step3: Sum up the derivatives

$f^\prime(x)=7x^{-8}+1+0=\frac{7}{x^{8}}+1$.

Answer:

$\frac{7}{x^{8}}+1$