# Is -1/2z the correct result for differentiating ln(3y-2z) with respect to z?

• cabellos
In summary, the conversation involved differentiating ln(3y-2z) with respect to z, and the resulting answer being -2/(3y-2z). The use of the chain rule was suggested and applied to get this answer.
cabellos
I should know this, but i just wanted to check...differentiating ln(3y-2z) with respect to z...does this = -1/2z ?

You must differentiate the whole thing first, then differentiate what is on the inside.

To check your answer take the integral of -1/2z, you will see it is not equal ln(3y-2z)

As KoGs suggested, an appropriate use of the chain rule should do just fine.

ok so is it -2/3y + z

cabellos said:
ok so is it -2/3y + z

No, it is not. As mentioned before, try to apply the chain rule:http://mathworld.wolfram.com/ChainRule.html"

Last edited by a moderator:
I did apply it...this is how i calculated that result:

d/dz In(3y-2z)
y=In u therefore dy/du = 1/u
u=3y-2z therefore du/dz = -2
dy/du x du/dz = -2/(3y-2z)

where am i going wrong?

cabellos said:
I did apply it...this is how i calculated that result:

d/dz In(3y-2z)
y=In u therefore dy/du = 1/u
u=3y-2z therefore du/dz = -2
dy/du x du/dz = -2/(3y-2z)

where am i going wrong?

Now you're not going wrong, since the result is correct. Good work!

## 1. What is differentiation check?

Differentiation check is a process used in mathematics to find the rate of change of a function at a specific point. It involves calculating the derivative of the function and evaluating it at the given point.

## 2. Why is differentiation check important?

Differentiation check is important because it allows us to analyze the behavior of a function and make predictions about its values. It is also a fundamental tool in calculus and is used to solve various real-world problems involving rates of change.

## 3. How do you perform a differentiation check?

To perform a differentiation check, you first need to find the derivative of the function. This can be done by using differentiation rules or formulas. Once you have the derivative, you can then plug in the given point to find the rate of change or slope at that point.

## 4. What is the difference between differentiation and integration?

Differentiation and integration are two fundamental operations in calculus. Differentiation involves finding the rate of change of a function, while integration involves finding the area under a curve. In other words, differentiation is used to find the slope of a curve, while integration is used to find the area between the curve and the x-axis.

## 5. What are some common applications of differentiation check?

Differentiation check has many applications in various fields such as physics, engineering, and economics. Some common applications include finding maximum and minimum values of a function, analyzing motion and acceleration, and optimizing production and profit functions in business.

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