derivative of ln & e

Question 1


y = e^(x^3) * ln x^2
dy/dx = {d[e^(x^3)] / dx}(ln x^2) + {d(ln x^2) / dx}[e^(x^3)]
= 3x^2[e^(x^3)](ln x^2) + (2x / x^2)[e^(x^3)]
= [e^(x^3)][3x^2(ln x^2) + (2 / x)]




Question 2

should be f(x) = (1 - e^x) / x, NOT x^2
f'(x) = {[d(1 - e^x) / dx]x - (dx / dx)(1 - e^x)} / x^2
= [-xe^x - (1 - e^x)] / x^2
= (-xe^x - 1 + e^x)] / x^2
= [e^x(1 - x) - 1] / x^2

[f(x)g(x)]'=f(x)'g(x)+f(x)g(x)'
[f(g(x))]'=f'(g(x))+g'(x)
1.
令f(x)=e^(x^3)
g(x)=lnx^2
f(x)'=3x^2×e^(x^3)
g(x)'=(1/x^2)×2x=2/x
∴y=[3x^2×e^(x^3)]×[lnx^2]+[e^(x^3)]×[2/x]
　 =e^(x^3)× [(3x^2 ln x^2) +2/x]

第2題, sorry,我也求不出你給的答案
如果我算出來會馬上補充的~^^