Find the derivative of: y=x^3/2 *(3ln(x)-2)

Thread starter fazal
Start date Dec 4, 2008
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Derivative

In summary, the function for which we need to find the derivative is y=x^3/2 *(3ln(x)-2). The procedure for finding the derivative of this function is to use the power rule and the product rule. The power rule states that the derivative of x^n is n*x^(n-1), while the product rule states that the derivative of f(x)*g(x) is f'(x)*g(x) + f(x)*g'(x). The derivative of ln(x) is 1/x and is used in this function by using the chain rule to find the derivative of 3ln(x). The significance of finding the derivative of a function is that it represents the rate of change of the function at a

Dec 4, 2008

fazal

Homework Statement

Find the derivative of:

y=x^3/2 *(3ln(x)-2)

Homework Equations

as above

The Attempt at a Solution

iam using product rule
dy/dx =[d/dx x^3/2]*(3ln(x)-2) + x^3/2 [d/dx(3ln(x)-2)]

how to solve ln differential ?

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Dec 4, 2008

Vagrant

This should help
http://www.mathcentre.ac.uk/resources/workbooks/mathcentre/web-logs-exp.pdf"

Last edited by a moderator: Apr 24, 2017

Dec 5, 2008

fazal

Thank u guys

What is the function for which we need to find the derivative?

The function is y=x^3/2 *(3ln(x)-2).

What is the procedure for finding the derivative of this function?

The procedure for finding the derivative of this function is to use the power rule and the product rule. First, we use the power rule to find the derivative of x^3/2, which is 3/2*x^(3/2-1) or 3/2*x^(1/2). Then, we use the product rule to find the derivative of the entire function, which is (3ln(x)-2)*3/2*x^(1/2) + x^3/2 * (3/x). Simplifying this will give us the final answer.

What is the general formula for the power rule and product rule?

The power rule states that the derivative of x^n is n*x^(n-1). The product rule states that the derivative of f(x)*g(x) is f'(x)*g(x) + f(x)*g'(x).

What is the derivative of ln(x) and how is it used in this function?

The derivative of ln(x) is 1/x. In this function, we use the chain rule to find the derivative of 3ln(x). This results in 3*(1/x), which simplifies to 3/x. This is then multiplied by the derivative of x^3/2 to get the final derivative of the function.

What is the significance of finding the derivative of a function?

The derivative of a function represents the rate of change of the function at a given point. It is used in many applications of calculus, such as finding the slope of a tangent line, optimizing functions, and solving related rates problems.