Question

hw 8 - derivative rules section 2.3: problem 6 (1 point)
find the derivative of the function $f(x)=2\frac{1}{x^{3}}+x^{2}+14$.
$f(x)=$
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Explanation:

Step1: Rewrite the function

Rewrite $2\frac{1}{x^{3}}$ as $2x^{- 3}$. So $f(x)=2x^{-3}+x^{2}+14$.

Step2: Apply power - rule for derivatives

The power - rule states that if $y = ax^{n}$, then $y^\prime=anx^{n - 1}$.
For $y = 2x^{-3}$, $y^\prime=2\times(-3)x^{-3 - 1}=-6x^{-4}$.
For $y = x^{2}$, $y^\prime=2x^{2 - 1}=2x$.
For $y = 14$ (a constant), $y^\prime = 0$.

Step3: Find the derivative of the whole function

$f^\prime(x)=-6x^{-4}+2x+0$.

Answer:

$- \frac{6}{x^{4}}+2x$