(b) if $y = \\frac{-3}{2}x^{4}$, find $\\frac{dy}{dx}$. $\\frac{dy}{dx}=\\square$
(b) if $y = \\frac{-3}{2}x^{4}$, find $\\frac{dy}{dx}$. $\\frac{dy}{dx}=\\square$
Answer
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:
$-6x^{3}$