f(x)=x∣x∣ and g(x)=sinxg∘f(x)=sin(x∣x∣)={−sinx2sinx2,x<0,x≥0∴ (gof )′(x)={−2xcosx22xcosx2,x<0,x≥0 Clearly, L(gof )' (0)=0=R( gof )′(0) ∴ gof is differentiable at x=0 and also its derivative is continuous at x=0 Now, (gof)" (x)={−2cosx2+4x2sinx22cosx2−4x2sinx2,x<0,x≥0∴L( gof )′′(0)=−2 and R( gof )′′(0)=2∴L( gof )′′(0)=R( gof )′′(0) ∴gof(x) is not twice differentiable at x=0.