Mathematics - Differentiation Question with Solution | TestHub

$$\begin{array}{rl}& f(x)=\sin (\sin x)\\ & \Rightarrow f^{\prime }(x)=\cos (\sin x)\cdot \cos x\\ & \Rightarrow f^{\prime \prime }(x)=-\sin (\sin x)\cdot {\cos }^{2}x+\cos (\sin x)\text{. }\\ & (-\sin x)\\ & =-{\cos }^{2}x\cdot \sin (\sin x)-\sin x\cdot \cos (\sin x)\\ & \text{ Now }{f}^{\prime \prime }(x)+\tan x.f^{\prime }(x)+g(x)=0\\ & \Rightarrow g(x)={\cos }^{2}x\cdot \sin (\sin x)+\sin x\cdot \cos (\sin x)\\ & -\tan x\cdot \cos x\cdot \cos (\sin x)\\ & \Rightarrow g(x)={\cos }^{2}x\cdot \sin (\sin x)\text{. }\\ & \end{array}$$