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differentiate the following function with respect to x (x^x) . (sqrt x)

differentiate the following function with respect to x
(x^x) . (sqrt x)

Grade:12

1 Answers

Rinkoo Gupta
askIITians Faculty 80 Points
8 years ago

Let y1=xx

Taking log on both sides, get

logy1=xlogx

Diff w. r. to x ,get

(1/y1). dy1/dx=x.1/x+logx.1

dy1/dx=y1[1+logx]

=xx[1+logx]

Now using Product rule of diff. to the give function

dy/dx=xx(1/2√x)+√x. xx(1+logx)

Thanks & Regards

Rinkoo Gupta

AskIITians Faculty

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