Solving derivative with roots in denominator

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SUMMARY

The discussion focuses on calculating the derivative of the function f(x) = 3/(sqrt(1+x^2)) using the limit definition of the derivative. The correct limit expression is lim as h approaches 0 of (f(x+h) - f(x))/h. Participants emphasize the importance of correctly simplifying the difference quotient and ensuring that the denominators of fractions are aligned before combining terms. The initial attempt at the solution contained errors in the difference quotient, which needed correction for accurate derivative computation.

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Homework Statement



i have to get f'(x) using the limit definition of the derivative (lim as h approches 0 f(x)= (f(x+h) - f(x)) /h) and I don't know where to start. f(x)= 3/(sqrt(1+x^2)

Homework Equations


what do I do with the (sqrt(1+x^2)


3. The attempt at a solution
I have gotten to lim as h approches 0 f(x)= (f(x+h) - f(x)) /h) = 3-3/ sqrt(1+(x+h)^2- sqrt(1-x^2)/h
 
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Uh, it's lim h->0 of (f(x+h)-f(x))/h. Your difference quotient is kind of messed up. Can you fix it up first?
 
I might add that the numerator won't be 3 - 3 as you show.

3/a - 3/b != (3 - 3)/(stuff in the denominator)

Before you start adding the terms in the numerators of fractions, the denominators have to be the same.
 

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