Question

is the derivative e^x^2 the same as the derivative e^2x? why doesnt this hold?

Answer 1

simply because
x^2 is NOT = 2x

those 2 are different function,
hence their derivative will also be different! :)

Answer 2

if you mean
e^(x^2) and e^(2x) then no but
e^x^2=e^(2x)

Answer 3

\((e^x)^2 = e^{2x} \)

Answer 4

Let \(t= e^x\)
so that if it is \((e^x)^2\), then it is \(t^2\)
if it is \(e^{2x} = e^{x+x} = e^x*e^x= t*t =t^2\)
So that I don't see why they are not the same @ikram002p

Answer 5

(e^x)^2 is indeed e^(2x)

but e^x^2 is not e^(2x)

infact, e^x^2 is ambiguous :P

Answer 6

a^b^c^b^e = \(a^{b^{c^{d^{e}}}} = a^{\left(b^{\left(c^{(d^{e})}\right)}\right)}\neq \left(\left((a^b)^c\right)^d\right)^e = a^{bcde}\)

So e^x^2 \(= e^{x^2}\neq(e^x)^2 = e^{2x}\)

Answer 7

this was the whole question:
determine the derivative of the function y(x) = ((e^x)^2) ln (2x + 0.5) in x=0

for the derivative of ((e^x)^2), the right answer was 2x. ((e^x)^2) but if i turned ((e^x)^2) into e^2x then the derivative would have been just 2.e^2x.

Answer 8

"the derivative of ((e^x)^2), the right answer was 2x. ((e^x)^2) "
Nopes.

(e^x)^2 does equal e^(2x)
and its derivative is
2 e^(2x)
and not 2x (e^x)^2

Answer 9

the derivative of

e^(x^2) will be
2x e^(x^2)

Answer 10

and e^(x^2) is not in your question

Answer 11

there are no brackets in the book so i'm kind a confused, it's 'e' powered to the x powered to 2

Answer 12

slope of two different things would different use simple logic