Question

find the derivative of the following function. g(t)=14\sqrt{t}
g(t)=□

Explanation:

Step1: Rewrite the function

Rewrite $\sqrt{t}$ as $t^{\frac{1}{2}}$, so $g(t)=14t^{\frac{1}{2}}$.

Step2: Apply power - rule

The power - rule for differentiation is $\frac{d}{dt}(at^n)=ant^{n - 1}$, where $a = 14$ and $n=\frac{1}{2}$.
$g'(t)=14\times\frac{1}{2}t^{\frac{1}{2}-1}$.

Step3: Simplify the expression

$14\times\frac{1}{2}=7$, and $\frac{1}{2}-1=-\frac{1}{2}$. So $g'(t)=7t^{-\frac{1}{2}}$.

Step4: Rewrite in radical form

$t^{-\frac{1}{2}}=\frac{1}{\sqrt{t}}$, so $g'(t)=\frac{7}{\sqrt{t}}$.

Answer:

$\frac{7}{\sqrt{t}}$