"Find the first and second derivatives. s=5t3−3t5" was answered by students like you

High School
Calculus and Analysis
Calculus 1
Derivatives

djeljenike

Answered question

2021-06-06

Find the first and second derivatives.

s = 5 t^{3} - 3 t^{5}

Answer & Explanation

Benedict

Skilled2021-06-07Added 108 answers

Use that derivative of $x^{n} i s n x^{(n - 1)}$
$\frac{d s}{d t} = \frac{d}{d t} (5 t^{3}) - \frac{d}{d t} (3 t^{5})$
$\frac{d s}{d t} = 5 (3 t^{3 - 1}) - 3 (5 t^{5 - 1})$
$\frac{d s}{d t} = 15 t^{2} - 15 t^{4}$
$\frac{d^{2} s}{{d t}^{2}} = \frac{d}{d t} (15 t^{2}) - \frac{d}{d t} (15 t^{4})$
$\frac{d^{2} s}{{d t}^{2}} = 15 (2 t^{2 - 1}) - 15 (4 t^{4 - 1})$
$\frac{d^{2} s}{{d t}^{2}} = 30 t - 60 t^{3}$

Answers is
$\frac{d s}{d t} = 15 t^{2} - 15 t^{4}$
$\frac{d^{2} s}{{d t}^{2}} = 30 t - 60 t^{3}$

Jeffrey Jordon

Expert2021-11-24Added 2605 answers

Answer is given below (on video)

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