Question

hw 8 - derivative rules section 2.3: problem 6 (1 point) results for this submission entered answer preview -2/(x^2)+2*x -\frac{2}{x^{2}} + 2x the answer above is not correct. find the derivative of the function f(x)=2\frac{1}{x^{1}}+x^{2}+14. f(x)=

Explanation:

Step1: Rewrite the function

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

Step2: Apply power - rule for derivatives

The power - rule states that if $y = ax^{n}$, then $y^\prime=anx^{n - 1}$.
For the first term $y_1 = 2x^{-1}$, $y_1^\prime=2\times(-1)x^{-1 - 1}=-2x^{-2}=-\frac{2}{x^{2}}$.
For the second term $y_2 = x^{2}$, $y_2^\prime=2x^{2 - 1}=2x$.
For the third term $y_3 = 14$ (a constant), $y_3^\prime = 0$.

Step3: Sum up the derivatives of each term

$f^\prime(x)=y_1^\prime + y_2^\prime+y_3^\prime=-\frac{2}{x^{2}}+2x+0=-\frac{2}{x^{2}}+2x$.

Answer:

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