Question

(b) if $y = \frac{-3}{2}x^{4}$, find $\frac{dy}{dx}$. $\frac{dy}{dx}=\square$

Explanation:

Step1: Recall power - rule for differentiation

The power - rule states that if $y = ax^n$, then $\frac{dy}{dx}=anx^{n - 1}$, where $a$ is a constant and $n$ is a real number. Here, $a=-\frac{3}{2}$ and $n = 4$.

Step2: Apply the power - rule

$\frac{dy}{dx}=-\frac{3}{2}\times4x^{4 - 1}$.

Step3: Simplify the expression

$-\frac{3}{2}\times4x^{3}=-6x^{3}$.

Answer:

$-6x^{3}$