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farukk
 3 years ago
Find dy\dx if y=(x+1)^x
farukk
 3 years ago
Find dy\dx if y=(x+1)^x

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RolyPoly
 3 years ago
Best ResponseYou've already chosen the best response.2\[y=(x+1)^x\]\[lny = xln(x+1)\]Diff. both sides w.r.t. x

farukk
 3 years ago
Best ResponseYou've already chosen the best response.0i have tried but failed in getting answer

RolyPoly
 3 years ago
Best ResponseYou've already chosen the best response.2Can you show your work?

farukk
 3 years ago
Best ResponseYou've already chosen the best response.0i have a few questions similar to it so explain also

RolyPoly
 3 years ago
Best ResponseYou've already chosen the best response.2\[y=(x+1)^x\]\[\ln y=x\ln(x+1)\]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.

robtobey
 3 years ago
Best ResponseYou've already chosen the best response.0Refer to the attachment.

RolyPoly
 3 years ago
Best ResponseYou've already chosen the best response.2\[\frac{1}{y} \frac{dy}{dx} = x\frac{d}{dx}(\ln (x+1))+ ln(x+1)\frac{d}{dx}x\]\[\frac{1}{y} \frac{dy}{dx} = x(\frac{1}{x+1})+ ln(x+1)(1)\]\[\frac{1}{y} \frac{dy}{dx} = (\frac{x}{x+1})+ ln(x+1)\]\[\frac{dy}{dx} = y[(\frac{x}{x+1})+ ln(x+1)]\]Then sub y= (x+1)^x into dy/dx
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