What is the derivative of #y=2tan^-1(e^x)#?

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Answer 1 · 2018-06-09T13:57:59

#(dy)/(dx)=(2e^x)/(1+e^(2x)#

Here,

#y=2tan^-1(e^x)#

Let,

#y=2tan^-1u and u=e^x#

#(dy)/(du)=2/(1+u^2) and (du)/(dx)=e^x#

#"Using "color(blue)"Chain Rule : "#

#color(blue)((dy)/(dx)=(dy)/(du)*(du)/(dx)#

#=>(dy)/(dx)=2/(1+u^2)xxe^x,where, u=e^x#

#=>(dy)/(dx)=(2e^x)/(1+(e^x)^2)#