Question

Найти производную
1) f (x)=x^3/e^x
2) f (x)=e^x/lnx

Answer 1

1)f'(x)=(3x^2*e^x-e^x*x^3)/e^(2x)
f'(x)=x^2*e^x*(3-x)/e^(2x)
f'(x)=x^2*(3-x)/e^x

2)f'(x)=(e^x*lnx-(1/x)*e^x)/ln^2(x)
f'(x)=e^x/lnx-e^x/(x*lnx)
f'(x)=e^x/lnx*(1-1/x)