Question

Find dy\dx if y=(x+1)^x

Answer 1

\[y=(x+1)^x\]\[lny = xln(x+1)\]Diff. both sides w.r.t. x

Answer 2

plz do it for me

Answer 3

i have tried but failed in getting answer

Answer 4

Can you show your work?

Answer 5

i have a few questions similar to it so explain also

Answer 6

yeah

Answer 7

did u use this?

Answer 8

\[y=(x+1)^x\]\[\ln y=x\ln(x+1)\]Diff. both sides w.r.t. x
\[\frac{1}{y} \frac{dy}{dx} = x\frac{d}{dx}(\ln (x+1))+ ln(x+1)\frac{d}{dx}x\]
Yes, product rule.

Answer 9

okay

Answer 10

Refer to the attachment.

Answer 11

thanks all

Answer 12

@RolyPoly

Answer 13

\[\frac{1}{y} \frac{dy}{dx} = x\frac{d}{dx}(\ln (x+1))+ ln(x+1)\frac{d}{dx}x\]\[\frac{1}{y} \frac{dy}{dx} = x(\frac{1}{x+1})+ ln(x+1)(1)\]\[\frac{1}{y} \frac{dy}{dx} = (\frac{x}{x+1})+ ln(x+1)\]\[\frac{dy}{dx} = y[(\frac{x}{x+1})+ ln(x+1)]\]Then sub y= (x+1)^x into dy/dx