Question

differentiate 2sinx with respect ex​

Answer 1

$\textbf{To find:}$

$\textsf{Derivative of 2 sinx with respect to}\;\mathsf{e^x}$

$\mathsf{That\,is,\,\dfrac{d(2\,sinx)}{d(e^x)}}$

$\textbf{Solution:}$

$\textbf{Formula used:}$

$\boxed{\begin{minipage}{4cm} \\\mathsf{\;\;\;\dfrac{d(sinx)}{dx}=cosx}\\\\\mathsf{\;\;\;\dfrac{d(e^x)}{dx}=e^x}\\ \end{minipage}}$

$\mathsf{Consider,}$

$\mathsf{\dfrac{d(2\,sinx)}{d(e^x)}}$

$\mathsf{=\dfrac{\dfrac{d(2\,sinx)}{dx}}{\dfrac{d(e^x)}{dx}}}$

$\mathsf{=\dfrac{\dfrac{2\,d(sinx)}{dx}}{\dfrac{d(e^x)}{dx}}}$

$\mathsf{=\dfrac{2\,cosx}{e^x}}$

$\implies\boxed{\mathsf{\dfrac{d(2\,sinx)}{d(e^x)}=\dfrac{2\,cosx}{e^x}}}$

$\textbf{Find more:}$

Find dy/dx y=cot^3[log(x^3)]​

https://brainly.in/question/16678493

If y=x+√(x²-1), then y-x(dy/dx) = ???

https://brainly.in/question/21230642

Answer 2

SOLUTION

TO DETERMINE

$\sf{Differentiate \: \: 2 \sin x \: \: with \: respect \: to \: \: {e}^{x} }$

EVALUATION

Let

$\sf{y = 2 \sin x}$

$\sf{z = {e}^{x} }$

Now

$\displaystyle \sf{ \frac{dy}{dx} = 2 \cos x}$

$\displaystyle \sf{ \frac{dz}{dx} = {e}^{x} }$

Hence the required differential

$\displaystyle \sf{ \frac{dy}{dz} }$

$\displaystyle \sf{ = \frac{dy}{dx} \: . \: \frac{dx}{dz} }$

$\displaystyle \sf{ = \frac{ \frac{dy}{dx}}{ \frac{dz}{dx}} }$

$\displaystyle \sf{ = \frac{2 \cos x}{ {e}^{x} } }$

$\displaystyle \sf{ = 2 \: {e}^{ - x}\cos x}$

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. Cos^-1(1-9^x/1+9^x) differentiate with respect to x

https://brainly.in/question/17839008

2. Find the nth derivative of sin 6x cos4x

https://brainly.in/question/29905039