Find and simplify the difference quotient of the function f (x) = (3x+1)/(4x) . Find the first derivative f′(x) from the definition, using the rules for limits.

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Find and simplify the difference quotient of the function f (x) = (3x+1)/(4x) . Find the first derivative f′(x) from the definition, using the rules for limits.

Mathematics
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f(x)= 3x/4x +1/4x = 3/4 + 1/4x f'(x)= lim [f(x+h)-f(x)]/h as h->0 f'(x)= lim (3/4 + 1/4(x+h) -3/4 - 1/4x) /h f'(x)= lim [(x-h-x)/(4x(h+x))]/h f'(x)= lim [-h/(4xh(x+h)]= lim (-1/(4x(x+h))] as h->0 f'(x)= -1/(4x^2) <-- answer
is that the derivative of the function or the difference quotient?
the first equation is difference quotient the last equation is the derivative

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Other answers:

aahh got it. i couldn't see the little dash. tanks again
not a problem
what happens to h at the end of the equation?
h goes to zero

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