Question

Question #54aa1

Answer 1

`(2e^(2x^2)(2x^2lnx-1))/(xln^3(x))`

Explanation:

for the quotient rule

`(e^(2x^2))/(Lnx)^2`

`d/dx((e^(2x^2))/(Lnx)^2)`

`d/dx((e^(2x^2))/(Lnx)^2)=(d/dx(e^(2x^2))(ln^2(x))-(e^(2x^2))d/dx(ln^2(x)))/(ln^2(x))^2`

`d/dx(e^(2x^2))=4x.e^(2x^2)`

`d/dx(ln^2(x))=2/xln(x)`

`d/dx((e^(2x^2))/(Lnx)^2)=((4x.e^(2x^2))(ln^2(x))-(e^(2x^2))2/xln(x))/(ln^2(x))^2`

multiplying everything for a x

`d/dx((e^(2x^2))/(Lnx)^2)=((4x^2.e^(2x^2))(ln^2(x))-(e^(2x^2))2ln(x))/(x(ln^2(x))^2`

factoring `e^(2x^2)(2ln(x))`

`d/dx((e^(2x^2))/(Lnx)^2)=(2e^(2x^2)ln(x)(2x^2lnx-1))/(xln^4(x))`

dividing

`d/dx((e^(2x^2))/(Lnx)^2)=(2e^(2x^2)(2x^2lnx-1))/(xln^3(x))`