Question

prove d/dx (1/u^n)= -n/u^n+1 * du/dx

Answer 1

\[\frac{1}{u^n}=u^{-n}\]
does that help?

Answer 2

chain rule here i guess. since we are assuming that
\(u=u(x)\) then \(y=u^{-n}\) and \(\frac{dy}{du}=-nu^{-n-1}\)
\[\frac{dy}{dx}=\frac{dy}{du}\times \frac{du}{dx}\]

Answer 3

@satellite73 how about this one prove d/dx (square root of u) = 1/2*square root of u * du/dx?? help me pls..

Answer 4

thank you..

Answer 5

it is pretty much as Satellite did before
\(u=u(x)\) and \(y=\sqrt{u}\) then
\[ \large \frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx} \]
where
\[ \large \frac{dy}{du}=\frac{1}{2\sqrt{u}} \]

Answer 6

where did u get u=u(x)?

Answer 7

it is a way of saying that \(u\) is a dependent variable and that it depends on \(x\)

Answer 8

your post are about the chain rule as Satellite pointed out.

Answer 9

yeah..right.. thank you..

Answer 10

did u get it?

Answer 11

yes i got it. thanks.

Answer 12

u r welcome.