Question

Differentiate 2[f(x)^3] with respect to x

Answer 1

I'm trying to see why it comes out to
\[\Large 6[f(x^2)]f \prime (x) \] and not \[\Large 6[f(x)^2]\]

Answer 2

@amistre64

Answer 3

@Hero

Answer 4

\[\frac{ d }{dx }\left\{ f ^{n} \left( x \right) \right\}=nf ^{n-1}\left( x \right)f'\left( x \right)\]
\[\frac{ d }{ dx }f \left( x ^{n} \right)=f'\left( x ^{n} \right)n x ^{n-1}\]

Answer 5

because of the chain rule

Answer 6

Is it like that cause of "the respect to x" why it's like that?

Answer 7

i think you want the proof for chain rule

Answer 8

you must work it out from first principles

Answer 9

Yes, please lol. I just started calc and Im asking this question from here: http://www.wikihow.com/Take-Derivatives-in-Calculus

Answer 10

okay well lets start with stating the chain rule first and then we will prove it

Answer 11

Ok