June 05, 2023, 09:13:57 pm

### AuthorTopic: Derivative Question  (Read 1158 times) Tweet Share

0 Members and 1 Guest are viewing this topic.

#### dummi

• Fresh Poster
• Posts: 4
• Respect: 0
##### Derivative Question
« on: July 10, 2022, 02:18:49 am »
0
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

• Science Games: Gold
• Forum Obsessive
• Posts: 300
• Respect: +127
##### 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)
VCE 2016-2018

2017: Biology [38], Further Maths [44]

2018: Methods [37], French [38], Chem [40], English [44]

UMAT: 56/43/80, 57th percentile (LLLLOOOOOOOOOLLLLLLLL)

ATAR: 98.1

2019-2021: Bachelor of Biomedical Science at Monash (Scholars), minoring in Chemistry

GAMSAT September 2021: 65/67/86, 76 overall (98th percentile)

2022: Chilling

2023+: Transfer to teaching degree

#### dummi

• Fresh Poster
• Posts: 4
• Respect: 0
##### Re: Derivative Question
« Reply #2 on: July 10, 2022, 11:28:36 am »
0
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

• Posts: 6
• Respect: +1
##### 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

• Trailblazer
• Posts: 41
• "I'm just trying to get myself some gravity";
• Respect: +6
##### Re: Derivative Question
« Reply #4 on: July 11, 2022, 09:21:14 pm »
0
Hi There - I think you have picked the wrong term for "u":

ex1/2
ex = u

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!
VCE 2021: Methods (42 raw), Biology (46 raw); 2022: Chemistry, English, Spec, Physics