find the derivative. simplify where possible

Question

 f(x)=e^x cosh x

Answer 1

f(x)=e^x cosh x

 

d/dx[e^x cosh(x)]
=d/dx[e^x]⋅cosh(x)+e^x⋅d/dx[cosh(x)]
=e^x . cosh(x)+sinh(x) . e^x
=e^x . sinh(x)+e^x . cosh(x)

Simplify:
e^x (sinh(x)+cosh(x))