Question

How do you find the derivative of `f(x)=e^(8x)+cos(x)sin(x)`?

Answer 1

`d /(d x) f(x)=8*e^(7x)*l n e+1-2sin^2 x`

Explanation:

`f(x)=e^(8x)+cos(x)sin(x)`

`d /(d x) f(x)=8*e^(7x)*l n e-sin x*sin x +cos x *cos x`

`d /(d x) f(x)=8*e^(7x)*l n e-sin^2 x+cos^2 x`

`cos^2 x=1-sin^2 x`

`d /(d x) f(x)=8*e^(7x)*l n e-sin^2 x+(1-sin^2 x)`

`d /(d x) f(x)=8*e^(7x)*l n e-sin^2 x+1-sin^2 x`

`d /(d x) f(x)=8*e^(7x)*l n e+1-2sin^2 x`