Differentiate the following function with respect to x: (e^(ex) + e^(-2x))/(e^(2x) - e^(-2x))

Question

Differentiate the following function with respect to x:

\(\cfrac{e^{e\mathrm x}+e^{-2\mathrm x}}{e^{2\mathrm x}-e^{-2\mathrm x}}\)

Answer 1

Let y = \(\cfrac{e^{e\mathrm x}+e^{-2\mathrm x}}{e^{2\mathrm x}-e^{-2\mathrm x}}\)

On differentiating y with respect to x, we get

We know \(\frac{d}{d\mathrm x}\)(e^x) = e^x

However, \(\frac{d}{d\mathrm x}\)(x) = 1