Question

y=(e^x^2)/(e^x-e^-x)
Помогите найти производную/похідну

Answer 1

$y=\frac{e^{x^2}}{e^{x}-e^{-x}}\\\\y'=\frac{2x\cdot e^{x^2}\cdot (e^{x}-e^{-x})-e^{x^2}\cdot (e^{x}+e^{-x})}{(e^{x}-e^{-x})^2}=\frac{2x\cdot e^{x^2+x}-2x\cdot e^{x^2-x}-e^{x^2+x}-e^{x^2-x}}{(e^{x}-e^{-x})^2}=\\\\=\frac{(2x-1)\cdot e^{x^2+x}-(2x+1)\cdot e^{x^2-x}}{(e^{x}-e^{-x})^2}$