Question

find the indicated derivative.
$\frac{dy}{dx}$ if $y = - 6x^{3/2}$
$\frac{dy}{dx}=square$

Explanation:

Step1: Recall power - rule for derivatives

The power - rule states that if $y = ax^n$, then $\frac{dy}{dx}=anx^{n - 1}$, where $a=-6$ and $n = \frac{3}{2}$.

Step2: Apply the power - rule

$\frac{dy}{dx}=-6\times\frac{3}{2}x^{\frac{3}{2}-1}$.

Step3: Simplify the expression

First, calculate $-6\times\frac{3}{2}=-9$. Then, calculate $\frac{3}{2}-1=\frac{3 - 2}{2}=\frac{1}{2}$. So, $\frac{dy}{dx}=-9x^{\frac{1}{2}}$.

Answer:

$-9x^{\frac{1}{2}}$