Question

hw10 differentiation rules 1 (targets c1, c5; §3.3)
score: 2/9 answered: 2/9
question 3
if (f(x)=6 + \frac{4}{x}+\frac{7}{x^{2}}), find (f(x)).
question help: video message instructor

Explanation:

Step1: Rewrite the function

Rewrite $f(x)=6 + \frac{4}{x}+\frac{7}{x^{2}}$ as $f(x)=6 + 4x^{-1}+7x^{-2}$.

Step2: Apply power - rule of differentiation

The power - rule states that if $y = ax^{n}$, then $y'=nax^{n - 1}$. For the constant term 6, its derivative is 0 since the derivative of a constant $C$ is 0. For the term $4x^{-1}$, its derivative is $4\times(-1)x^{-1 - 1}=-4x^{-2}$. For the term $7x^{-2}$, its derivative is $7\times(-2)x^{-2 - 1}=-14x^{-3}$.

Step3: Combine the derivatives

$f'(x)=0-4x^{-2}-14x^{-3}$.

Answer:

$-\frac{4}{x^{2}}-\frac{14}{x^{3}}$