differentiate the following function with respect to x

(x^x) . (sqrt x)

Let y₁=x^x

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]

=x^x[1+logx]

Now using Product rule of diff. to the give function

dy/dx=x^x(1/2√x)+√x. x^x(1+logx)

Thanks & Regards

Rinkoo Gupta

AskIITians Faculty