Question

Differentiate -: e^(-x)sin x ​

Answer 1

Step-by-step explanation:

Enter a problem...

Calculus Examples

Popular Problems

 

Calculus

Find the Derivative - d/dx (e^x)/(sin(x))

exsin(x)exsin(x)

Differentiate using the Quotient Rule which states that ddx[f(x)g(x)]ddx[f(x)g(x)] is g(x)ddx[f(x)]−f(x)ddx[g(x)]g(x)2g(x)ddx[f(x)]-f(x)ddx[g(x)]g(x)2where f(x)=exf(x)=ex and g(x)=sin(x)g(x)=sin(x).

sin(x)ddx[ex]−exddx[sin(x)]sin2(x)sin(x)ddx[ex]-exddx[sin(x)]sin2(x)

Differentiate using the Exponential Rule which states that ddx[ax]ddx[ax] is axln(a)axln(a) where aa=ee.

sin(x)ex−exddx[sin(x)]sin2(x)sin(x)ex-exddx[sin(x)]sin2(x)

The derivative of sin(x)sin(x) with respect to xx is cos(x)cos(x).

sin(x)ex−excos(x)sin2(x)sin(x)ex-excos(x)sin2(x)

Reorder factors in sin(x)ex−excos(x)sin(x)ex-excos(x).

Answer 2

Answer:

Differentiate using the Exponential Rule which states that ddx[ax] d d x [ a x ] is axln(a) a x ln ( a ) where a =e . The derivative of sin(x) with respect to x is cos(x) .

Explanation:

Since this is a product of 2 functions we may apply the product rule which states that the derivative of a product of 2 functions is the first function times the derivative of the second, plus the second function times the derivative of the first