HSC Stuff > HSC Mathematics Extension 1

Help with Derivatives

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RuiAce:

--- Quote from: JKFlacka on February 12, 2017, 11:15:27 am ---Oh wow... I'm stuck again :/

According to the textbook:
If f(x)=g(x)+h(x), then
f'(x)=g'(x)+h'(x)

Question
Differentiate: f(x)=4x^2-3x+2

Why is this wrong?
f'(x)= 4(2x)-3(x^0)+2
f'(x)=8x-3+2
f'(x)=8x-1

But the actual answer is 8x-3. Does the two get ignored or something?

Also, how do I make that beautiful looking type font for math?

:D

--- End quote ---
The derivative of 2 is 0. Everything else was good.

This is my LaTeX guide. There's more of these floating around the internet.

Dragomistress:
I would like someone to show me the working out as the textbook doesn't show the substitution for dy/dx and I am confused on how this substitution works. Please show through 1a.

Thanks

kiwiberry:

--- Quote from: JKFlacka on February 13, 2017, 08:39:14 pm ---I would like someone to show me the working out as the textbook doesn't show the substitution for dy/dx and I am confused on how this substitution works. Please show through 1a.

Thanks

--- End quote ---

Dragomistress:
Cool, thanks for the replies :D Best forum of my life.

May someone show me the quickest way to do this question (just so that I can verify and potentially upgrade my working).

[This is a chain rule derivative question]

Shadowxo:

--- Quote from: JKFlacka on February 14, 2017, 08:59:55 pm ---Cool, thanks for the replies :D Best forum of my life.

May someone show me the quickest way to do this question (just so that I can verify and potentially upgrade my working).

[This is a chain rule derivative question]

--- End quote ---

Great answer by M909! :)
Just a little extra:
dy/dx = dy/du * du/dx.
Let's say u = px + q
y = u8
dy/du = 8u7
du/dx = p
dy/dx = 8u7*p = 8p(px+q)7
So if you've got anything inside a bracket to a power that you need to derive, you derive the bracket section, treating what's inside as u then multiplying by the derivative of the bracket
eg 2(3x2+6x+12)5
derivative is 2*5(3x2+6x+12)4*(6x+6)

Hope this helps :)

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