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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: dummi on July 10, 2022, 02:18:49 am

Title: Derivative Question
Post by: dummi on July 10, 2022, 02:18:49 am
Pls how do you solve this I'm literally so confused

d/dx (e√x)

My working got to here
ex1/2
ex = u
u1/2
1/2 * u-1/2 *ex

and then when I googled it they made u = x or sumn idek but the answer supposed to be:
e√x/2√x

PLS HELP  :'( :'( :'( :'(
Title: Re: Derivative Question
Post by: Billuminati on July 10, 2022, 03:55:11 am
Pls how do you solve this I'm literally so confused

d/dx (e√x)

My working got to here
ex1/2
ex = u
u1/2
1/2 * u-1/2 *ex

and then when I googled it they made u = x or sumn idek but the answer supposed to be:
e√x/2√x

PLS HELP  :'( :'( :'( :'(

By chain rule it will be derivative of outer function (e√x) multiplied by the derivative of the inner function (x0.5)

dy/dx = [e√x ] * [0.5 * x-0.5]
dy/dx = e√x * 1/2 * 1/√x = e√x / (2√x)
Title: Re: Derivative Question
Post by: dummi on July 10, 2022, 11:28:36 am
By chain rule it will be derivative of outer function (e√x) multiplied by the derivative of the inner function (x0.5)

dy/dx = [e√x ] * [0.5 * x-0.5]
dy/dx = e√x * 1/2 * 1/√x = e√x / (2√x)

Why is the inner function x0.5 and not ex0.5
Title: Re: Derivative Question
Post by: hvo-ade on July 10, 2022, 06:11:20 pm
Pls how do you solve this I'm literally so confused

d/dx (e√x)

My working got to here
ex1/2
ex = u
u1/2
1/2 * u-1/2 *ex

and then when I googled it they made u = x or sumn idek but the answer supposed to be:
e√x/2√x

PLS HELP  :'( :'( :'( :'(
You got the function u wrong. See the attachment below.
Title: Re: Derivative Question
Post by: RaspberryTau on July 11, 2022, 09:21:14 pm
Hi There - I think you have picked the wrong term for "u":

ex1/2
ex = u

Instead you should do:
u = x^1/2

This is because the "e" is the outer function. It's just the notation is slightly different to usual.

Eg - when finding the derivative for tan(x^2) - tan is the outer function. (The one that is applied last).

Eg2. When deriving e^(x^2); the order is:
1. x
2. x^2
3. ex^2

So the outer function is e^.....;

In ur question, say we let f(x) = e^x;
Then the expression becomes: f( x^1/2 )

Hope this helps! :)