Trouble with manipulating indices (differentiation) (1 Viewer)

Zeref · Jul 27, 2013

I have tried googling for some explanations about changing the forms of f(x) to a differentiable form. An example would be differentiating sqrt of x. the f'(x) would be 1/2 x^-1/2
but i dont understand why that turns into 1/2 sqrt x.

another example is what would happen if there was a fraction in front e.g
f'(x)= 6/5 x^-7/8

what are the steps that need to be taken so that the answer looks nice or in simplest form.

sorry about typing the numbers up like that, its rly quite hard to see ><

SpiralFlex · Jul 27, 2013

Zeref said:
I have tried googling for some explanations about changing the forms of f(x) to a differentiable form. An example would be differentiating sqrt of x. the f'(x) would be 1/2 x^-1/2
but i dont understand why that turns into 1/2 sqrt x.

another example is what would happen if there was a fraction in front e.g
f'(x)= 6/5 x^-7/8

what are the steps that need to be taken so that the answer looks nice or in simplest form.

sorry about typing the numbers up like that, its rly quite hard to see ><

$y = \sqrt{x}$

[HR][/HR]

$First I want to highlight something. Let's assume that$\; m\; $and$\; n \;$are positive and$\; n \;$is not equal to zero. Then these forms are equal.$

[HR][/HR]

$$We note,$\; \frac{d}{dx} x^n = nx^{n-1}, \;$for$\; n \neq -1$

$Mentally, we think of this as multiplying the front by the original power, then taking away one from the exponent.$

[HR][/HR]

$$Equivalently, try rewritting to$\; y= x^{\frac{1}{2}}$

$y={\color{Red} \frac{1}{2}}x^{{\color{Blue} \frac{1}{2}-1}} \textup{{\color{Red}\; We multiply the front by the original power} AND {\color{Blue} we subtract one from the exponent}}$

$= \frac{1}{2}x^{-\frac{1}{2}}$

$Using the forms we have described:$

$y'=\frac{1}{2\sqrt{x}}$

[HR][/HR]

$Can you now try if:$ \; y = \frac{6}{5}x^{-\frac{7}{8}}\; $by emulating what I did?$

Zeref · Jul 27, 2013

$Can you now try if:$ \; y = \frac{6}{5}x^{-\frac{7}{8}}\; $by emulating what I did?$ [/QUOTE]

first off i'd like to thank you SOOOOOOO much for using up your time and effort to explain it to me

is the answer is 6/ 5 (subscript 8) sqrt x^7 ?

lol i really need to learn how to use latex

Smile12345 · Jul 27, 2013

Zeref said:
lol i really need to learn how to use latex

Same... I'll do it with you!

SpiralFlex · Jul 27, 2013

Uh, nope. try again. Read carefully what I wrote in red and blue. You'll get it, just keep trying.

SpiralFlex · Jul 27, 2013

I will show you another example perhaps.

$y=\frac{1}{3}x^{-\frac{1}{3}}$

$y'={\color{Red} -\frac{1}{3}}*\frac{1}{3}x^{-\frac{1}{3}{\color{Blue} -1}} \textup{{\color{Red}\; We multiply the front by the original power in this case, -1/3} AND {\color{Blue} we subtract one from the exponent}}$

$y'=-\frac{1}{9}x^{-\frac{4}{3}}$

Smile12345 · Jul 27, 2013

SpiralFlex said:
I will show you another example perhaps.

$y=\frac{1}{3}x^{-\frac{1}{3}}$

$y'={\color{Red} -\frac{1}{3}}*\frac{1}{3}x^{{\color{Blue} -\frac{1}{3}-1}} \textup{{\color{Red}\; We multiply the front by the original power} AND {\color{Blue} we subtract one from the exponent}}$

$y'=-\frac{1}{9}x^{-\frac{4}{3}}$

Now I'm new to latex and not sure if I've done it right... but here is my answer for the other question asked...

$y' = -\frac{21}{20}x^{-\frac{15}{8}}$

SpiralFlex · Jul 27, 2013

Smile12345 said:
Now I'm new to latex and not sure if I've done it right... but here is my answer for the other question asked...

$y' = -\frac{21}{20}x^{-\frac{15}{8}}$

That's the correct answer.

Zeref · Jul 27, 2013

SpiralFlex said:
That's the correct answer.

OH i just realised u wanted me to find y' *facepalm*

the only problem i had was just the converting of the indices haha
assuming ur question was rewriting y, would i be correct?

Smile12345 · Jul 27, 2013

SpiralFlex said:
That's the correct answer.

Awesome...

SpiralFlex, Can you please help me with some questions?

SpiralFlex · Jul 27, 2013

Zeref said:
OH i just realised u wanted me to find y' *facepalm*

the only problem i had was just the converting of the indices haha
assuming ur question was rewriting y, would i be correct?

Uhm, the reason I showed you the image wasn't for the question. It was because I thought you needed help with changing things around (and that may have lead you to understand the question better)

SpiralFlex · Jul 27, 2013

Smile12345 said:
Awesome... SpiralFlex, Can you please help me with some questions?

Inbox me.

Smile12345 · Jul 27, 2013

SpiralFlex said:
Inbox me.

Ok...

RealiseNothing · Jul 27, 2013

Zeref said:
first off i'd like to thank you SOOOOOOO much for using up your time and effort to explain it to me

is the answer is 6/ 5 (subscript 8) sqrt x^7 ?

lol i really need to learn how to use latex

you are correct.

Trouble with manipulating indices (differentiation) (1 Viewer)

Zeref

Stare into my eyes.

SpiralFlex

Well-Known Member

Zeref

Stare into my eyes.

Smile12345

Active Member

SpiralFlex

Well-Known Member

SpiralFlex

Well-Known Member

Smile12345

Active Member

SpiralFlex

Well-Known Member

Zeref

Stare into my eyes.

Smile12345

Active Member

SpiralFlex

Well-Known Member

SpiralFlex

Well-Known Member

Smile12345

Active Member

RealiseNothing

what is that?It is Cowpea

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