Question

please solve this question ​

Answer 1

Given:

$\\ \pink\bigstar\rm{Differentiate \: e^{\sqrt{3x}} \: with \: respect \: to \: x}$

To Find :

$\\ \pink\bigstar\rm{Differentiation \: of \: given \: expression=?}$

Solution:

• Consider a function y=f(x) , where f(x) is a given expression in the question

According to the given conditions :

By using Chain's Rule:

$\\ \implies \sf \: y = {e}^{ \sqrt{3x} }$

$\\ \\ \implies \underline{ \red{ \bf{differentiating \: \: both \: \: side \: \: with \: respect \: to \: x}}}$

$\\ \implies \sf \: \frac{dy}{dx} = {e}^{ \sqrt{3x} } \times \frac{1}{2 \sqrt{3} x} \times 3 \\ \\ \implies \sf \: \frac{dy}{dx} = \frac{3y}{2 \sqrt{3} x } \\ \\ \implies \boxed{\boxed{ \sf{ \frac{dy}{dx} = \frac{3y}{2 \sqrt{3} x} }}}$

$\pink\bigstar\rm{Differentiation \: of \: e^{\sqrt{3x}} \: is \: \dfrac{3y}{2\sqrt{3}x}}$