Best solutions to - "Find the first and second derivatives. r=13s2−74s3 drds="

Reggie

Answered question

2021-05-25

Find the first and second derivatives.

r = \frac{1}{3 s^{2}} - \frac{7}{4 s^{3}}

\frac{d r}{d s} =

wornoutwomanC

Skilled2021-05-26Added 81 answers

Step 1
The given functions r(s) is

r = \frac{1}{3 s^{2}} - \frac{7}{4 s^{3}}

r = \frac{1}{3} s^{- 2} - \frac{7}{4} s^{- 3}

Step 2
Formula used: Power rule of derivative

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

Step 3
The

1^{s t}

derivative can be evaluated as

r = \frac{1}{3} s^{- 2} - \frac{7}{4} s^{- 3}

Differentiating both side w.r.t. s, gives

\frac{d r}{d s} = \frac{1}{3} \cdot (- 2 s^{- 2 - 1} - \frac{7}{4} (- 3 s^{- 3 - 1}))

\frac{d r}{d s} = - \frac{2}{3} s^{- 3} + \frac{21}{4} s^{- 4}

Step 4
The

2^{n d}

derivative can be evaluated by differentiating again on both the side of above

1^{s t}

derivative function as shown below:

\frac{d^{2} r}{d s^{2}} = - \frac{2}{3} \cdot (- 3 s^{- 3 - 1}) + \frac{21}{4} (- 4 s^{- 4 - 1})

\frac{d^{2} r}{d s^{2}} = 2 s^{- 4} - 21 s^{- 5}

Step 5
Answer:
The

1^{s t}

derivative is

\frac{- 2}{3 s^{- 3}} + \frac{21}{4 s^{- 4}}

The

2^{n d}

derivative is

2 s^{- 4} - 21 s^{- 5}

Jeffrey Jordon

Expert2021-11-24Added 2605 answers

Answer is given below (on video)

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