Derivative of 4/sqrt{x}: Step-by-Step Guide

MHB
Thread starter schooler
Start date Oct 5, 2014
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Derivative

In summary, a derivative is a mathematical concept used to represent the rate of change of a function at a specific point. To find the derivative of a fraction, you can use the quotient rule or the power rule. Most scientific calculators have the ability to find derivatives. The purpose of finding the derivative is to gain insight into the behavior of a function and its real-world applications.

Oct 5, 2014

schooler

Steps for finding the derivative of 4/sqrt{x}

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Oct 5, 2014

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MHB

schooler said:

Steps for finding the derivative of 4/sqrt{x}

Write it as $\displaystyle \begin{align*} 4x^{-\frac{1}{2}} \end{align*}$ and you should be able to continue :)

Related to Derivative of 4/sqrt{x}: Step-by-Step Guide

1. What is a derivative?

A derivative is a mathematical concept that represents the rate of change of a function at a specific point. It is commonly used in calculus to find the slope of a tangent line to a curve at a given point.

2. How do I find the derivative of a fraction?

To find the derivative of a fraction, you can use the quotient rule, which states that the derivative of f(x)/g(x) is (g(x)f'(x) - f(x)g'(x)) / (g(x))^2. In the case of 4/sqrt(x), the derivative would be (sqrt(x)(0) - 4(1/2x^(-1/2))) / (sqrt(x))^2, which simplifies to -2/x^(3/2).

3. What do I do with the square root in this equation?

In order to find the derivative of 4/sqrt(x), you can rewrite the equation as 4x^(-1/2) and then use the power rule, which states that the derivative of x^n is nx^(n-1). In this case, the derivative would be -2x^(-3/2).

4. Can I use a calculator to find the derivative?

Yes, most scientific calculators have the ability to find derivatives of functions. You can input the function 4/sqrt(x) and use the appropriate function or button to find the derivative at a specific point or as a general equation.

5. What is the purpose of finding the derivative of a function?

The derivative of a function can provide valuable information about the behavior of the function. It can help us find the slope of a curve, identify maximum and minimum points, and determine the rate of change of a function. Derivatives are also used in many real-world applications, such as physics, engineering, and economics.