a2linetagadaW

2021-10-04

Derivatives Find and simplify the derivative of the following functions

$y=\frac{{w}^{4}+5{w}^{2}+w}{{w}^{2}}$

grbavit

Skilled2021-10-05Added 109 answers

Step 1

Given:$y=\frac{{w}^{4}+5{w}^{2}+w}{{w}^{2}}$

Step 2

Explanation:

$y=\frac{{w}^{4}+5{w}^{2}+w}{{w}^{2}}$

We can re-write it as

$y=\frac{{w}^{4}}{{w}^{2}}+\frac{5{w}^{2}}{{w}^{2}}+\frac{w}{{w}^{2}}$

$y={w}^{2}+5+\frac{1}{w}$

$y={w}^{2}+5+{w}^{-1}$

Differentiate both sides with respect to w , we get

$\frac{dy}{dw}=\frac{d}{dw}({w}^{2}+5+{w}^{-1})$

$\frac{dy}{dw}=\frac{d}{dw}\left({w}^{2}\right)+\frac{d}{dw}\left(5\right)+\frac{d}{dw}\left({w}^{-1}\right)$

$\frac{dy}{dw}=2w+0+(-1){w}^{-1-1}\text{}\text{}\text{}[\because \frac{d}{dx}\left({x}^{n}\right)=n{x}^{n-1}]$

$\frac{dy}{dw}=2w-{w}^{-2}$

$\frac{dy}{dw}=2w-\frac{1}{{w}^{2}}$

$\frac{dy}{dw}=\frac{2{w}^{3}-1}{{w}^{2}}$

Given:

Step 2

Explanation:

We can re-write it as

Differentiate both sides with respect to w , we get

Jeffrey Jordon

Expert2022-08-15Added 2575 answers