What is the derivative of $(5x)/e^x$ ?

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Answer 1 · 2016-09-05T14:56:37

$dy/dx=5e^-x(1-x)$ .

Let $y=5x/e^x=5x*e^-x$

$:. dy/dx=d/dx(5x*e^-x)=5d/dx(x*e^-x)$ .

$:. dy/dx=5[x*d/dx(e^-x)+e^-x*d/dx(x)]$

$=5{x*e^-x*d/dx(-x)+e^-x*1].............."[Chain Rule]"$

$=5(-xe^-x+e^-x)$

$:. dy/dx=5e^-x(1-x)$ .

Alternatively , using Quotient Rule ,

$dy/dx=5d/dx(x/e^x)=5{(e^xd/dx(x)-xd/dx(e^x))/(e^x)^2}$

$=5((e^x-xe^x)/(e^x)^2)=5((e^x(1-x))/(e^x)^2)=(5(1-x))/e^x$

$:. dy/dx=5e^-x(1-x)$ , as before!

Enjoy Maths.!

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