If y=sincossinx, then dydx=
-coscossinxsincosxcosx
-coscossinxsinsinxcosx
coscossinxsincosxcosx
coscossinxsinsinxcosx
Explanation for the correct option:
Finding the value of dydx:
Given that,
y=sincossinx
Using Chain Rule, Differentiating with respect to x both sides:
dydx=coscos(sinx)×ddxcos(sinx)∵du·vdx=udvdx+vdudx⇒dydx=coscos(sinx)×-sin(sinx)×ddx(sinx)∵dsinxdx=cosx,dcosxdx=-sinx⇒dydx=-coscos(sinx)sin(sinx)cosx
Hence, Option (B) is the correct answer.