Question

derivative of sin under root x ....

Answer 1

Assume you mean

y=sinx√x

Write it as y=sin(x1/2). Then use this chain rule formula:

d/dxsinu=cosudu/dx.

Letting the inside function be

u=x1/2

get that

dy/dx=d/dxsin(x1/2)

=cos(x1/2)d/dxx1/2

=cos(x1/2)1/2x1/2−1

=1/2x−1/2cos(x1/2)

=1/2x1/2cos(x1/2)

=1/2x−−√cosx−−√