Let `f(x)` be a differentiable and let `c` a be a constant. Then `cf(x)` is also differentiable such that `d/(dx){cf(x)}=c d/(dx)(f(x))dot`

Explanation

We know that

`f'(x)=lim_(h->0)=(f(x+h)-f(x))/h`

=`d/(dx)(f(x))`

let `g(x)=cf(x)`

`g'(x)=d/dx(c(f(x)))=lim_(h->0)=(g(x+h)-g(x))/h`

so,`g'(x)=lim_(h->0)=(cf(x+h)-cf(x))/h`

=`clim_(h->0)=(f(x+h)-f(x))/h`

=`cd/(dx)(f(x))`

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