Question

Differentiate
\[f(x)=\sqrt{12x-x^3}\]

Answer 1

(x)
= lim h -> 0 [f(x + h) - f(x)] / h
= lim h -> 0 [ (x + h)^3 - 12(x + h) - x^3 + 12x] / h
= lim h -> 0 [ x^3 + 3x^2h + 3xh^2 + h^3 - 12 x - 12h - x^3 + 12x ] / h
= lim h-> 0 [ 3x^2h + 3xh^2 + h^3 - 12h ] / h
=lim h -> 0 (3x^2 + 3xh + h^2 - 12)
= 3x^2 - 12

Answer 2

http://answers.yahoo.com/question/index?qid=20080512124800AAOkysi

Answer 3

@billie4120 Do you know chain rule?

Answer 4

\[\frac{d}{dx} (f(g(x))=f'(g(x))\times g'(x)\]

Answer 5

ok yes
so

Answer 6

here
\[f(x)=\sqrt x\]
\[g(x)=12x-x^3\]
Try now :)