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

1 Answer
Feb 6, 2017

Answer:

#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#