Expert answers to "Derivatives Find and simplify the derivative of the..." - Plainmath

Falak Kinney

Answered question

2021-10-23

Derivatives Find and simplify the derivative of the following functions

s (t) = \frac{t^{\frac{4}{3}}}{e^{t}}

Answer & Explanation

au4gsf

Skilled2021-10-24Added 95 answers

Step 1

s (t) = \frac{t^{\frac{4}{3}}}{e^{t}}

\frac{d s}{d t} = \frac{e^{t} \frac{d {(t)}^{\frac{4}{3}}}{d t} - t^{\frac{4}{3}} \frac{d (e^{t})}{d t}}{e^{2 t}}

Step 2

\frac{d s}{d t} = \frac{\frac{4}{3} e^{t} {(t)}^{\frac{4}{3}} - t^{\frac{4}{3}} e^{t}}{e^{2 t}}

= e^{t} \frac{4 {(t)}^{\frac{4}{3}} - 3 {(t)}^{\frac{4}{3}}}{3 e^{2 t}}

= \frac{4 {(t)}^{\frac{4}{3}} - 3 {(t)}^{\frac{4}{3}}}{3 e^{t}}

Jeffrey Jordon

Expert2022-08-14Added 2605 answers

Answer is given below (on video)

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