Derivative of e^x-e^-xexex?

3 Answers
Mar 10, 2018

e^x+e^-xex+ex

Explanation:

color(red)(d/(dx)(e^x)=e^xddx(ex)=ex
y=e^x-e^-x=>(dy)/(dx)=e^x-e^-x*d/(dx)(-x)y=exexdydx=exexddx(x)=e^x-e^-x(-1)=e^x+e^-x=exex(1)=ex+ex

Mar 10, 2018

e^x+e^(-x)ex+ex

Explanation:

"differentiate "e^(-x)" using the "color(blue)"chain rule"differentiate ex using the chain rule

"Given "y=f(g(x))" then"Given y=f(g(x)) then

dy/dx=f'(g(x))xxg'(x)larrcolor(blue)"chain rule"

rArrd/dx(e^(-x))=e^(-x)xxd/dx(-x)=-e^(-x)

rArrd/dx(e^x-e^(-x))

=e^x-(-e^(-x))=e^x+e^(-x)

Mar 10, 2018

=e^x+e^-x

Explanation:

d/dx(e^x-e^-x)
=d/dx(2sinh x) (definition of sinh x)
=2cosh x (Because d/dx sinhx = cosh x and vice versa)
=e^x+e^-x (definition of cosh x)