If *f*(*x*) and *g(x)* are differentiable functions at *x = a,* then following holds good

*k*is always differentiable (*f*(*x*)*k*is finite) at*x = a*Since**Proof:***f*(*x*) is differentiable at*x = a*finite and real

∴

*kf*is differentiable at*x = a*is always differentiable at*f*(*x*) ± g(x)*x = a*Let**Proof:***ψ(x) =**f*(*x*) + g(x)=

*f'(a*= finite^{+}) + g'(a^{+})∵

*f'(a*^{–}) = f'(a^{+}) and g'(a^{–}) = g'(a^{+})∴ L.H.D = R.H.D at x = a for ψ(

*x*)Thus ( ...

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