Pls help maths urgent

In product rule you’re meant to add the functions not subtract one from the other.

Thanks a lot! So i corrected that and got 0= -2x^4e^(-x^2) + 3x^2e^(-x^2)
Not sure how to simplify this though -could you pls kindly help with this as well

Yeah sure, basically you want to divide everything by e^(-x^2) which you’re allowed to do because that function never equals zero.

I don't quite get that - I thought you never cancel out something which has a variable in it e.g. x in this case
And am not sure about what you said about the function never equaling zero and also how its related.
lemme know please

Ok I’m going to have to get into some deep technical stuff here so bear with me xD.

So the reason you never cancel something with a variable is that you lose solutions if it equals zero.

So for x^2 = 7x I cant divide by x because I lose the solution x=0.

For sin^2(x) = 4cos(x)sin(x) I can’t divide by sin(x) because I lose the solution sin(x)=0.

However in the case of e^(-x^-2) this function can never be zero so we are allowed to cancel it.

If you’re not convinced then factorise it by taking out a factor of e^(x^-2) and then solve what’s in the brackets. Obviously if the bit inside the brackets = 0 then that’s a solution. The bit outside the brackets has no solutions because e^(-x^2) can never be zero.

Ah thanks a lot -never knew that! Ik it's pretty late so nw if not possible but if you do get the chance..how do you do 9 iv A -it's from the same question

Thanks a lot again