Explained: "Find the indicated derivatives. drds if r=s3−2s2+3" - Plainmath

aflacatn

Answered question

2021-09-22

Find the indicated derivatives.

\frac{d r}{d s} if r = s^{3} - 2 s^{2} + 3

Answer & Explanation

Alannej

Skilled2021-09-23Added 104 answers

Step 1
Given,

r = s^{3} - 2 s^{2} + 3

To find:

\frac{d r}{d s}

Solution:

r = s^{3} - 2 s^{2} + 3

Differentiating both sides w.r.t s we get:

\frac{d r}{d s} = \frac{d}{d s} (s^{3} - 2 s^{2} + 3)

\Rightarrow \frac{d r}{d s} = \frac{d}{d s} (s^{3}) - \frac{d}{d s} (2 s^{2}) + \frac{d}{d s} (3)

\Rightarrow \frac{d r}{d s} = 3 s^{2} - 2 (2 s) + 0

(using,

\frac{d}{d x} (x^{n}) = n x^{n - 1}

)

\Rightarrow \frac{d r}{d s} = 3 s^{2} - 4 s

Step 2
Result:

\frac{d r}{d s} = 3 s^{2} - 4 s

Jeffrey Jordon

Expert2022-01-31Added 2605 answers

Answer is given below (on video)

Jeffrey Jordon

Expert2022-02-01Added 2605 answers

Answer is given below (on video)

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