"Derivatives Find and simplify the derivative of the..." solved and explained

midtlinjeg

Answered question

2021-10-20

Derivatives Find and simplify the derivative of the following functions
$f (x) = e^{x} \sqrt{x^{3}}$

Answer & Explanation

Luvottoq

Skilled2021-10-21Added 95 answers

Step 1
Given $f (x) = e^{x} \sqrt{x^{3}}$
We need to find the derivative and simplify the above function.
Step 2
Using product rule to find the derivative
$f^{'} (x) = u v^{'} + v u^{'}$
where $u = e^{x} and v = \sqrt{x^{3}} = x^{\frac{1}{3}}$
$f^{'} (x) = e^{x} \frac{1}{3} x^{\frac{1}{3} - 1} + x^{\frac{1}{3}} e^{x}$
$f^{'} (x) = e^{x} \frac{1}{3} x^{\frac{- 2}{3}} + x^{\frac{1}{3}} e^{x}$
$f^{'} (x) = e^{x} [\frac{1}{3 x^{\frac{2}{3}}} + x^{\frac{1}{3}}]$
$f^{'} (x) = e^{x} [\frac{1 + 3 x \frac{1 + 2}{3}}{3 x^{\frac{2}{3}}}]$
$f^{'} (x) = e^{x} [\frac{1 + 3 x}{3 x^{\frac{2}{3}}}]$

Jeffrey Jordon

Expert2022-08-15Added 2605 answers

Answer is given below (on video)

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