Question

Differentiation help. *question below*

Answer 1

Can I have some help on this, please?

Answer 2

First, find the derivative (you'll need the product rule for this one):\[y=x^n\ln x~~\implies~~\frac{dy}{dx}=\cdots\]
Then plug this result into the equation and check if it holds:
\[\begin{align*}x(\cdots)&=x^n+ny\\
&=x^n+nx^n\ln x\end{align*}\]

Answer 3

\[\frac{ dy }{ dx }=nx ^{n-1}lnx + x ^{n-1}\]

Answer 4

Right, now sub that into the equation and see if you have an identity.

Answer 5

\[x(nx ^{n-1}lnx + x ^{n-1})\]
Hmm, I don't see an identity :s

Answer 6

\[x\left(\color{red}{nx ^{n-1}lnx + x ^{n-1}}\right)\]
Try distributing that black \(x\) to the other terms.

Answer 7

\[n^{n-1} x^n \ln(x)+x^n\]
?

Answer 8

Close, that factor of \(n\) is not raised to anything.

Answer 9

\[nx^n \ln(x)+x^n\]
is correct

Answer 10

Ah, I see

Answer 11

Hm, how do I proceed from here? @SithsAndGiggles

Answer 12

just realize that x^nlnx=y
replace that by y and you get what you want

Answer 13

Thank you so much!

Answer 14

Wow :D

Answer 15

welcome!

Answer 16

Math is so much awesome than WOW!

Answer 17

haha!