Mathematics - Continuity - Differentiability Question with Solution | TestHub

If$x^3-x \ge 0 \Rightarrow \cos \left|x^3-x\right|=\cos \left(x^3-x\right)$
$x^3-x<0 \Rightarrow \cos \left|x^3-x\right|=\cos \left(x^3-x\right)$
Similarly$b\left|x\right|\sin \left|x^3+x\right|=bx\sin \left(x^3+x\right)$for all$x\in R$
$\therefore$$f\left(x\right)=a\cos \left(x^3-x\right)+bx\sin \left(x^3+x\right)$
Which is composition and sum of differentiable functions therefore always continuous and differentiable.