Differentiate each of the following functions with respect to x.

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

Question

Differentiate each of the following functions with respect to x.

(i) $$e^{x^3}$$
(ii)$${-1\over2}x^{(1/2)^2}$$

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

Yes, but why?

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

Ok, I understand. How about the second one?

anonymous · Answer

$$x^{(-1/2)^2}$$

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

sorry $$e^{(-1/2)x^2}$$

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

Oh. Ok

anonymous · Answer

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