How do you find the derivative of the function using the definition of derivative #f(x) = 10#?

1 Answer

#f'(x) =0#

Explanation:

The derivative of a function is a measure of the rate of change of the function.

In this case the function is not changing as10 is a constant.

if f(x) = c where c is a constant then f'(x) = 0 The derivative of a constant is always zero.

EDIT: Definition added

Limit definition

The definition of the derivative:

#(df(x))/dx=lim_(h->0)(f(x+h)-f(x))/h#

Note: Since there is no #x# to substitute for #x+h#, no difference is noticed:

#lim_(h->0)(f(x+h)-f(x))/h=lim_(h->0)(10-10)/h=lim_(h->0)(0/h)=0#

So the derivative is equal to zero.