Hi there i need to show that the the deferential of
y=(3e^x^2) + (x^2)
is equal to
Thanks! i have an exam tomorrow so if you could be rly kind, please help me
Just in case a picture helps...
... where (key in spoiler) ...
Don't integrate - balloontegrate!
Balloon Calculus; standard integrals, derivatives and methods
Balloon Calculus Drawing with LaTeX and Asymptote!
I presume you mean 3e^(x^2) rather than, say, 3(e^x)^2 since that would be written 3e^(2x). Please use parentheses!
However, you cannot prove that the derivative of 3e^(x^2)+ x^2 is x(x e^(x^2)+ 2) because that is simply not true.
The derivative of e^u, where u is any function of x, is e^u(u'). In particular, The derivative of 3e^(x^2) is 3e^(x^2)(2x)= 6x e^(x^2). Of course, the derivative of x^2 is 2x so the derivative of 3e^(x^2)+ x^2 is 6x e^(x^2)+ 2x. You can factor out "2x" to get 2x(3e^(x^2)+ 1) which is NOT x(xe^x^2 +2).