How do you use the definition of a derivative to find the derivative of f(x)=5xf(x)=5x?

1 Answer
mason m
Dec 3, 2016

The limit definition of the derivative tells us that the derivative of a function is ff is

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

For this, f(x)=5x and f(x+h)=5(x+h), so:

f'(x)=lim_(hrarr0)(5(x+h)-5x)/h

color(white)(f'(x))=lim_(hrarr0)(5x+5h-5x)/h

color(white)(f'(x))=lim_(hrarr0)(5h)/h

color(white)(f'(x))=lim_(hrarr0)5

color(white)(f'(x))=5

So when f(x)=5x, we see that its derivative is f'(x)=5.

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