Expert Answer to "Find the derivatives of the functions s=−115(15t−1)3"

College
Calculus and Analysis
Differential Calculus
Derivatives

Khadija Wells

Answered question

2021-10-02

Find the derivatives of the functions

s = - \frac{1}{15} {(15 t - 1)}^{3}

Answer & Explanation

Dora

Skilled2021-10-03Added 98 answers

Step 1
Given:
$s = \frac{- 1}{15 {(15 t - 1)}^{3}}$
Step 2
Solution:
$s = \frac{- 1}{15 {(15 t - 1)}^{3}}$
$s = \frac{- 1}{15} {(15 t - 1)}^{3}$
Step 3
Derivative with respect to t
$\frac{d s}{d t} = \frac{- 1}{15} \frac{d}{d t} [{(15 t - 1)}^{3}]$
$\frac{d s}{d t} = \frac{- 1}{15} [3 {(15 t - 1)}^{2} \frac{d}{d t} (15 t - 1)] \Rightarrow [\begin{matrix} \frac{d}{d x} x^{n} = n x^{n - 1} \frac{d}{d x} x ∖ \frac{d}{d x} x^{n} = n x^{n - 1} (1) \end{matrix}]$
$\frac{d s}{d t} = \frac{- 1}{15} [3 {(15 t - 1)}^{2} (15)]$
$\frac{d s}{d t} = \frac{- 45}{15} {(15 t - 1)}^{2}$
$\frac{d s}{d t} = - 3 {(15 t - 1)}^{2}$

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