Question

Differentiation of sin(sinx)

Answer 1

Answer:

ddxsin(sinx)=cos(sinx)⋅cosx

Explanation:

The rule says that the derivative of the sine of a function is the cosine of the function multiplied by the derivative of the function,

∴ddxsinu(x)=cosu(x).dudx,

and so the result follows.

Answer 2

let y = sin ( sinx )
put u = Sinx ---(i) , then y = sin (u)----(ii)
Differentiate (ii) with respect to 'u' gives
dy / du = Cos(u) ----(iii)
Now differentiate (i) with respect to x gives
du / dx = Cos (x) ----(iv)
On multiplying (iii) and (iv) gives
(dy/du) × (du/dx) = {Cos (u) } × {Cos (x) }
=> dy/dx = [Cos(Sinx)] × {Cosx}