Question

Differentiate each of the following functions with respect to x.

(i) \[e^{x^3}\]
(ii)\[{-1\over2}x^{(1/2)^2}\]

Answer 1

Sorry, the (II) has no -1/2 infront

Answer 2

\[\left( e ^{x ^{3}} \right)\prime ===> 3x ^{2}e ^{x ^{3}}\]

Answer 3

Yes, but why?

Answer 4

e^(x^3) ->e^(x^3) * (x^3)' = 3x^2 * e^(x^3)

Answer 5

the derivative of e^x is itself times the derivative of x
in this case x is x^3

Answer 6

and derivative of X^3 is 3*x^2

Answer 7

When you have, e^(something), the derivative is e^(something) multiplied by the derivative of something

Answer 8

Ok, I understand. How about the second one?

Answer 9

\[x^{(-1/2)^2}\]

Answer 10

is that x^((-1/2)^2)

Answer 11

tell me if im wrong but is that just -1/2 x^1/4 to simplify? then you just find that derivative

Answer 12

sorry \[e^{(-1/2)x^2}\]

Answer 13

e^n derivative is e^n * n'
where n = (-1/2)*x^2
n'= -x

Answer 14

\[(e ^{(-1/2)x ^{2}})\prime ===> e ^{(-1/2)x ^{2}}(-x)\]

Answer 15

Oh. Ok

Answer 16

derivative of e^(_x)=-e^(-x)
ans=(-1/2)e^(-1/2)x^2{-x}=(1/2)e^(-1/2)x^2