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Differentiate xx+1 with respect to x. ...

Differentiate xx+1 with respect to x. 

A.

xx+1

B.

1x+1

C.

1x(x+1)2

D.

1(x+1)2

Correct answer is D

ddx(xx+1) = vdudxudvdxv2 

u = x, dudx = 1, v = x + 1, dvdx = 1

= (x+1)(1)x(1)(x+1)2 

= x+1x(x+1)2

= 1(x+1)2