Home > Calculus > Power Rule

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

Answer 1

Paisley Johnson

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

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#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Evelyn Agard

To find the derivative of the function ( f(x) = mx + b ), where ( m ) and ( b ) are constants:

[ f'(x) = \frac{d}{dx}(mx + b) = m ]

The derivative of a linear function ( mx + b ) with respect to ( x ) is simply the coefficient of ( x ), which is ( m ).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.