How do you find the derivative of the function f(x)=mx+bf(x)=mx+b?

1 Answer
Oct 19, 2016

using the definition of differentiation we have f'(x)=m

Explanation:

The definition of the derivative is:

f'(x)=Lim_(hrarr0)(f(x+h)-f(x))/h

f'(x)=Lim_(hrarr0)(m(x+h)+b-(mx+b))/h

f'(x)==Lim_(hrarr0)(mx+mh+b-mx-b)/h

f'(x)==Lim_(hrarr0)(cancel(mx)+mh+cancel(b)-cancel(mx)-cancel(b))/h

f'(x)==Lim_(hrarr0)(mcancel(h))/cancel(h)

f'(x)==Lim_(hrarr0)(m)

:.f'(x)=m