Question

Differentiate w.r.t. x: (e2x + e-2x)/(e2x - e-2x)

Answer 1

$y=\frac{e^{2x}+e^{-2x}}{e^{2x}-e^{-2x}}\\\\y=\frac{e^{2x}+1/e^{2x}}{e^{2x}-1/e^{2x}}\\\\y=\frac{e^{4x}+1}{e^{4x}-1}\\\\y(e^{4x}-1)=e^{4x}+1\\\\ye^{4x}-y=e^{4x}+1$
now differentiate with respect to x
$\frac{dy}{dx}e^{4x}+4ye^{4x} -\frac{dy}{dx}=4e^{4x}-0\\\\\frac{dy}{dx}(e^{4x}-1)=4e^{4x}(1-y)\\\\\frac{dy}{dx}=\frac{4e^{4x}(1-y)}{e^{4x}-1}$

Answer 2

HOPE IT WILL HELP YOU.

THANKS