Question

How do you differentiate `f(x)=e^x/sinx-cosx/e^x` using the quotient rule?

Answer 1

`(df)/dx = ((e^(2x)+sin^2x)(sinx-cosx))/(e^xsin^2x )`

Explanation:

`(df)/dx = d/dx e^x/sinx - d/dx cosx/e^x`

`(df)/dx = (e^xsinx-e^xcosx)/sin^2x - (-e^xsinx - e^xcosx)/e^(2x)`

`(df)/dx = e^x ((sinx-cosx)/sin^2x + (sinx - cosx)/e^(2x))`

`(df)/dx = e^x (e^(2x)(sinx-cosx)+ sin^2x(sinx - cosx))/(e^(2x)sin^2x )`

`(df)/dx = ((e^(2x)+sin^2x)(sinx-cosx))/(e^xsin^2x )`