Chapter 4.1, Problem 19E

To determine

To calculate : The differentiation of the given function.

Answer to Problem 19E

The differentiation is $\frac{-3}{{(2x+1)}^{\frac{3}{2}}}$ .

Explanation of Solution

Given information: Given function is $y=\frac{3}{\sqrt{2x+1}}$ .

Formula used: $\frac{d(x^n)}{dx}=n{x}^{n-1}\text{and}\frac{d(\text{constant})}{dx}=0$ with chain and addition rule.

Calculation:

  $y=\frac{3}{\sqrt{2x+1}}$

Differentiate with respect to x :

  $\begin{array}{l}\frac{dy}{dx}=3\times \frac{d{(2x+1)}^{\frac{-1}{2}}}{d(2x+1)}\times \frac{d(2x+1)}{dx}\\ $ \frac{dy}{dx}=3\times (\frac{-1}{2}{(2x+1)}^{\frac{-3}{2}})\times 2$\frac{dy}{dx}=\frac{-3}{{(2x+1)}^{\frac{3}{2}}}\end{array}$