Question

d/dx√xsinx=....... 0 < x< π,Select Proper option from the given options.
(a) xsinx+cosx/√xsinx
(b) xcosx/2√xsinx
(c) xcosx+sinx/2√xsinx
(d) 1/2√xsinx

Answer 1

we have to find the value of d{√(x.sinx)}/dx

d{√{x sinx}/dx = d{x.sinx}½/dx

= 1/2 (xsinx)^{1/2 - 1} × d(xsinx)/dx

= 1/2√(x.sinx) × [x d(sinx)/dx + sinx. dx/dx]

= 1/2√(x.sinx) × [x × cosx + sinx]

= 1/2√(x.sinx) [ x.cosx + sinx]

hence, option (c) is correct.

Answer 2

In the attachment I have answered this problem.         I have applied chain rule and product rule to find derivative of the given function.    Option C is correct   See the attachment for detailed solution.