Question

y=e^(1/(x+5))/(x+5)^2 найти производную

Answer 1

$y=frac{e^{frac1{x+5}}}{(x+5)^2}\y'=frac{left(e^{frac1{x+5}}right)'cdot(x+5)^2-e^{frac1{x+5}}cdotleft((x+5)^2right)'}{(x+5)^4}=\=frac{e^{frac1{1+5}}cdotleft(frac1{x+5}right)'cdot(x+5)^2-e^{frac1{x+5}}(2x+10)}{(x+5)^4}=\=frac{e^{frac1{x+5}cdotleft(-frac1{(x+5)^2}cdot(x+5)^2-(2x+10)right)}}{(x+5)^4}=-frac{e^{frac1{x+5}}cdotleft(1+2x+10right)}{(x+5)^4}=-e^{frac1{x+5}}cdotfrac{2x+11}{(x+5)^4}$