differentiate the function.\ny = \\frac{1}{(6x - 1)^3}\n\\frac{dy}{dx}=\\square
differentiate the function.\ny = \\frac{1}{(6x - 1)^3}\n\\frac{dy}{dx}=\\square
Answer
Explanation:
Step1: Rewrite the function
Rewrite $y=\frac{1}{(6x - 1)^3}$ as $y=(6x - 1)^{-3}$.
Step2: Apply the chain - rule
The chain - rule states that if $y = u^n$ and $u$ is a function of $x$, then $\frac{dy}{dx}=n\cdot u^{n - 1}\cdot\frac{du}{dx}$. Here, $n=-3$ and $u = 6x-1$, and $\frac{du}{dx}=6$. So, $\frac{dy}{dx}=-3\cdot(6x - 1)^{-3 - 1}\cdot6$.
Step3: Simplify the expression
$\frac{dy}{dx}=-3\cdot6\cdot(6x - 1)^{-4}=-18(6x - 1)^{-4}=-\frac{18}{(6x - 1)^4}$.
Answer:
$-\frac{18}{(6x - 1)^4}$