# How Do You Find the Derivative of log(x^2+y^3)?

• engstudent363
In summary, the conversation was about finding the derivative of log(x^2+y^3) and the different methods for solving it. The participants suggest using a calculus book or the chain rule and caution against expecting others to do the work for them. It is also mentioned that if x and y are both independent variables, a partial derivative should be used. The original poster is reminded that this question was asked 34 months ago and should have been resolved by now.
engstudent363
Derivative of log(x^2+y^3) ?

I'm familiar with the derivative of log x but not when x is raised to a power or when y is involved. Could someone offer some help? And if you know of a website that fully explains this please let me know. Thanks.

What is the general rule for taking a derivative of something in the form f(g(x)) ?

I don't know, and I never will unless you tell me.

engstudent363 said:
I don't know, and I never will unless you tell me.

Do you have a calculus book? Have you ever used it? The derivative of a function of the form f(g(x)) is a very important topic and will certainly be covered in a calculus book, you shouldn't expect people to do your work for you.

engstudent363 said:
I don't know, and I never will unless you tell me.
Guess you'll never learn a damn thing.

chain rule my friend. chain rule

engstudent363 said:
I'm familiar with the derivative of log x but not when x is raised to a power or when y is involved. Could someone offer some help? And if you know of a website that fully explains this please let me know. Thanks.

if x and y are both independent variable then you have to go for partial derivative.

thenabforlife and amaresh92: I strongly suspect that the original poster has been able to solve this problem somewhere along the line during the 34 months that have transpired since posting the problem. If not, the OP has bigger problems than the kind of help you two are offering.

Because sleeping threads should be left alone, I am locking this thread.

## 1. How do you find the derivative of log(x^2+y^3)?

The derivative of log(x^2+y^3) can be found using the chain rule, product rule, and quotient rule. First, we rewrite the equation as log(u), where u = x^2+y^3. Then, we use the chain rule to find the derivative of u, which is 2x+3y^2. Next, we use the product rule to find the derivative of log(u), which is (1/u)(du/dx). Finally, we use the quotient rule to find the derivative of (1/u), which is (-1/u^2)(du/dx). Combining these results, we get the final derivative of log(x^2+y^3) as (2x+3y^2)/(x^2+y^3).

## 2. Why is the derivative of log(x^2+y^3) important?

The derivative of log(x^2+y^3) is important because it allows us to find the rate of change of a function, which is useful in many real-world applications such as physics, economics, and engineering. It also helps us to find critical points and inflection points of the function, which can give us valuable information about the behavior of the function.

## 3. Can the derivative of log(x^2+y^3) be simplified?

Yes, the derivative of log(x^2+y^3) can be simplified by factoring out common terms in the numerator and denominator. In some cases, it may also be possible to simplify the expression using algebraic manipulations.

## 4. What is the domain of the derivative of log(x^2+y^3)?

The domain of the derivative of log(x^2+y^3) is the same as the domain of the original function, which is all real numbers except for x = 0 and y = 0. This is because the natural logarithm function is only defined for positive numbers, and if either x or y is 0, the function would be undefined.

## 5. How can the derivative of log(x^2+y^3) be used to solve real-world problems?

The derivative of log(x^2+y^3) can be used to solve optimization problems, where we want to find the maximum or minimum value of a function. It can also be used to find the slope of a curve at a specific point, which is important in physics and engineering problems. Additionally, it can help us to understand the behavior of a function and make predictions about its future values.

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