differentiate-the-following-functions-a-f-x-2x-5-coshx-

Question Number 74933 by imelder last updated on 04/Dec/19

differentiate the following functions

a) f (x) = {2 x}^{5} coshx

Commented by mathmax by abdo last updated on 04/Dec/19

f (x) = 2 x^{5} c h (x) = 2 x^{5} \times \frac{e^{x} + e^{- x}}{2} = x^{5} (e^{x} + e^{- x}) \Rightarrow

f^{^{'}} (x) = 5 x^{4} (e^{x} + e^{- x}) + x^{5} (e^{x} - e^{- x}) = (5 x^{4} + x^{5}) e^{x} + (5 x^{4} - x^{5}) e^{- x}

a n o t h e r w a y f^{^{'}} (x) = 10 x^{4} c h (x) + 2 x^{5} s h (x)