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December 01, 2022, 02:53:48 pm

Author Topic: Derivative Question  (Read 694 times)  Share 

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dummi

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Derivative Question
« on: July 10, 2022, 02:18:49 am »
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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  :'( :'( :'( :'(

Billuminati

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Re: Derivative Question
« Reply #1 on: July 10, 2022, 03:55:11 am »
+1
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)
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dummi

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Re: Derivative Question
« Reply #2 on: July 10, 2022, 11:28:36 am »
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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

hvo-ade

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Re: Derivative Question
« Reply #3 on: July 10, 2022, 06:11:20 pm »
+2
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.

RaspberryTau

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Re: Derivative Question
« Reply #4 on: July 11, 2022, 09:21:14 pm »
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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! :)
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