# Solving derivative with roots in denominator

• reggiehaft
In summary, the problem is to find f'(x) using the limit definition of the derivative, but the difference quotient used is incorrect. The correct expression for the difference quotient is (f(x+h) - f(x))/h, and the denominator must be the same for both fractions before adding the terms in the numerator.
reggiehaft

## 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

Last edited:
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.

## 1. What is a derivative with roots in the denominator?

A derivative with roots in the denominator is a type of mathematical expression that involves taking the derivative of a function that has a root or square root in the denominator. This can make the derivative more complex and require additional steps to solve.

## 2. How do I solve a derivative with roots in the denominator?

To solve a derivative with roots in the denominator, you will need to use the Quotient Rule of differentiation. This involves finding the derivative of the numerator and denominator separately, and then combining them using a specific formula. You may also need to use algebraic manipulation to simplify the expression before taking the derivative.

## 3. Why is it important to know how to solve derivatives with roots in the denominator?

Understanding how to solve derivatives with roots in the denominator is important because it allows you to find the instantaneous rate of change of a function at a specific point. This is a fundamental concept in calculus, and is used in many real-world applications such as physics, engineering, and economics.

## 4. What are some common mistakes when solving derivatives with roots in the denominator?

One common mistake when solving derivatives with roots in the denominator is forgetting to use the Quotient Rule and instead using the Power Rule. This can lead to incorrect solutions. Another mistake is not simplifying the expression before taking the derivative, which can make the process more complicated and prone to errors.

## 5. Can I use a calculator to solve derivatives with roots in the denominator?

While some calculators have the capability to solve derivatives, it is important to understand the concept and steps involved in solving derivatives with roots in the denominator by hand. This will not only help you better understand the concept, but also allow you to catch any potential errors made by the calculator. However, once you have a good understanding of the concept, using a calculator can be a helpful tool to check your work and save time.

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