Question

if (f(x)=2+\frac{8}{x}+\frac{7}{x^{2}}), find (f(x)).

Explanation:

Step1: Rewrite the function

Rewrite $f(x)$ as $f(x)=2 + 8x^{-1}+7x^{-2}$.

Step2: Apply power - rule for differentiation

The power - rule states that if $y = ax^n$, then $y'=nax^{n - 1}$. For the constant term $2$, its derivative is $0$ since the derivative of a constant is $0$. For the term $8x^{-1}$, its derivative is $-1\times8x^{-1 - 1}=-8x^{-2}$. For the term $7x^{-2}$, its derivative is $-2\times7x^{-2 - 1}=-14x^{-3}$.

Step3: Combine the derivatives

$f'(x)=0-8x^{-2}-14x^{-3}$.

Step4: Rewrite in original form

$f'(x)=-\frac{8}{x^{2}}-\frac{14}{x^{3}}$.

Answer:

$f'(x)=-\frac{8}{x^{2}}-\frac{14}{x^{3}}$