Question

question
find the derivative of (y = 7x^{2sqrt{x}}).
provide your answer below:
(y=square)

Explanation:

Step1: Recall power - rule for derivatives

The power - rule states that if $y = ax^n$, then $y'=anx^{n - 1}$, where $a$ is a constant and $n$ is a real number. Here, $a = 7$ and $n=\frac{2}{3}$.

Step2: Apply the power - rule

$y'=7\times\frac{2}{3}x^{\frac{2}{3}-1}$.

Step3: Simplify the exponent

$\frac{2}{3}-1=\frac{2 - 3}{3}=-\frac{1}{3}$. So, $y'=\frac{14}{3}x^{-\frac{1}{3}}$.

Answer:

$\frac{14}{3}x^{-\frac{1}{3}}$