"Derivatives Find and simplify the derivative of the..." was answered by our community

a2linetagadaW

Answered question

2021-10-04

Derivatives Find and simplify the derivative of the following functions

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

Answer & Explanation

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{d y}{d w} = \frac{d}{d w} (w^{2} + 5 + w^{- 1})

\frac{d y}{d w} = \frac{d}{d w} (w^{2}) + \frac{d}{d w} (5) + \frac{d}{d w} (w^{- 1})

\frac{d y}{d w} = 2 w + 0 + (- 1) w^{- 1 - 1} [∵ \frac{d}{d x} (x^{n}) = n x^{n - 1}]

\frac{d y}{d w} = 2 w - w^{- 2}

\frac{d y}{d w} = 2 w - \frac{1}{w^{2}}

\frac{d y}{d w} = \frac{2 w^{3} - 1}{w^{2}}

Jeffrey Jordon

Expert2022-08-15Added 2575 answers

Answer is given below (on video)

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