To determine
To calculate:
y'
Answer
y'= -sinx.cos(cosx)
Explanation
Rule:
i. Chain rule:
ddxy=dydu.dudx
ii.
ddx(sinx)=cosx
iii.
ddx(cosx)= -sinx
Given:
y= sin(cosx)
Calculation:
y= sin(cosx)
Let y=sinu
Where u=cosx
Differentiate y with respect to x
y'=ddxsincosx
By using chain rule
y'=ddu(sinu).dudx
By using ddx(sinx)=cosx
y'=(cosu).dudx
Substitute value of u
y'= coscosx.ddx(cosx)
By using rule ddx(cosx)= -sinx
y'= coscosx.(-sinx)
By rearrangement
y'= -sinx.cos(cosx)
Conclusion:
y'= -sinx.cos(cosx)