Answer to Question #228414 in Calculus for Sarah

Question

Y = In ( e^x + e^-x ) ; a = In^3

Answer 1

The question is incomplete but we can find derivative here.

$y=ln(e^x+e^{-x}) \\\Rightarrow \dfrac{dy}{dx}=\dfrac{d}{dx}(ln(e^x+e^{-x})) \\\Rightarrow \dfrac{dy}{dx}=\dfrac{1}{e^x+e^{-x}}\times \dfrac{d}{dx}(e^x+e^{-x}) \\\Rightarrow \dfrac{dy}{dx}=\dfrac{1}{e^x+e^{-x}}\times(e^x-e^{-x}) \\\Rightarrow \dfrac{dy}{dx}=\dfrac{e^x-e^{-x}}{e^x+e^{-x}}$