Is This Derivative Calculation Correct?

Thread starter neutron star
Start date Oct 18, 2009
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Derivative

In summary, a derivative is a mathematical concept used to measure the instantaneous rate of change of a function. It is important because it allows for analysis and predictions of function behavior, and is used in various real-world applications. Derivatives can be calculated using different formulas depending on the type of function, and it is different from a differential, which is a notation used to represent the derivative. While an expert in derivatives, there may be multiple correct ways to approach a derivative problem.

Oct 18, 2009

neutron star

Homework Statement

[tex]y= 4^x + 9/x^3[/tex]

Homework Equations

The Attempt at a Solution

[tex]y'= ln(4)4^x-27x^-^4[/tex]

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Oct 18, 2009

Whiz

That's correct.

1. What is a derivative?

A derivative is a mathematical concept that represents the instantaneous rate of change of a function with respect to one of its variables. In simpler terms, it measures how much a function is changing at a specific point.

2. Why is the derivative important?

The derivative is important because it allows us to analyze the behavior of functions and make predictions about their future values. It is also used in many real-world applications, such as physics, economics, and engineering.

3. How do you calculate a derivative?

The derivative is calculated using a specific formula, depending on the type of function. For simple functions, such as polynomials, the derivative can be found by using the power rule. For more complex functions, techniques like the chain rule, product rule, or quotient rule may be needed.

4. What is the difference between a derivative and a differential?

A derivative is a mathematical concept, while a differential is a notation used to represent the derivative. In other words, the derivative is the concept and the differential is the symbol (usually denoted by dx).

5. Can you check my answer for a derivative problem?

Yes, as a scientist, I am familiar with derivatives and their calculations. However, it is important to note that there may be different ways to approach a derivative problem, so while I can provide feedback, my answer may not necessarily be the only correct one.