How do you use the definition of a derivative to find the derivative of f(x)=1/3x+4/5?

1 Answer
Jim G.
Feb 6, 2017

f'(x)=1/3

Explanation:

Using the color(blue)"limit definition"

color(red)(bar(ul(|color(white)(2/2)color(black)(f'(x)=lim_(hto0)(f(x+h)-f(x))/h)color(white)(2/2)|)))

rArrf'(x)=lim_(hto0)(1/3(x+h)+4/5-(1/3x+4/5))/h

=lim_(hto0)(cancel(1/3x)+1/3hcancel(+4/5)cancel(-1/3x)cancel(-4/5))/h

=lim_(hto0)(1/3cancel(h)^1)/cancel(h)^1=1/3

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