Thread: differentiation

1. differentiation

i know this is a simple differentiation, but i just can't remember how to do it!
can someone please differentiate

((x^3)+3(x^2)+1) ^(1/3)

also how can i write x^2 on this forum so it looks like how x^2 should look, with a superscript 2.

2. Hello, mathmonster!

You need the Chain Rule . . .

$f(x) \;=\;\left(x^3+3x^2+1\right)^{\frac{1}{3}}$

$f'(x)\;=\;\frac{1}{3}\left(x^3+3x^2+1\right)^{-\frac{2}{3}}(3x^2 +\, 6x) \;=\;\frac{3x^2+6x}{3(x^3+3x^2+1)^{\frac{2}{3}}} \;=\;\frac{x^2+2x}{(x^3+3x+1)^{\frac{2}{3}}}$

3. Originally Posted by mathmonster
also how can i write x^2 on this forum so it looks like how x^2 should look, with a superscript 2.
Left-click on the script that Soroban wrote in his answer. That will show you how to code it.

There is a thread on how to use LaTeX in one of the subforums. (Or you could do a web search. Tips on how to code are all over it.)

-Dan

4. $
\log_{5} 25=2
$

just checking now to see how this works

5. $
f(x) = (x^3+3x^2+1)^{\frac{1}{3}}
$

6. Originally Posted by mathmonster
$
f(x) = (x^3+3x^2+1)^{\frac{1}{3}}
$
Looks like you've got it!

-Dan

how can i write simple differentiations in latex

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