Question

11. Find dy/dx for the following:-
1. y=(x+ sinx)cos x
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Answer 1

y =xcosx+sinxcosx

=xcosx+sin2x/2

dy/dx= x(-sinx)+cosx+(1/2×2cos2x)

=cos2x+cosx-xsinx

By using product rule,

d(xcosx)/dx=x(dcosx/dx)+cosx (dx/dx)

=X(-sinx)+cosx

we have the formula,

sin2x=2sinxcosx

sinxcosx=sin2x/2

d(sinxcosx)/dx=d(sin2x/2)/dx

=1/2(2cos2x)=cos2x

Answer 2

Heya mate......

here is your answer ✌️.....

dy/dx

d{(X+sinx)cosx}/dx

by applying product rule we get

(X+sinx)×d(cosx)/dx + cosx×d(X+sinx)/dx

(X+sinx)×-sinx +cosx×(1+cosx)

xsinx-sin2x + cosx+ cos2x