# Having troubles getting this derivative

• bmed90
In summary, a derivative is a mathematical concept used to calculate the rate of change of one variable with respect to another. It is important in various fields of science and can be calculated using differentiation rules. Some common mistakes when finding derivatives include forgetting the chain rule and making algebraic errors. Real-world applications of derivatives include predicting stock market trends, calculating object speed and acceleration, and modeling complex systems in fields like engineering, biology, and medicine.
bmed90

## Homework Statement

find dx/dt and dy/dt

## Homework Equations

x= sin(t)-tcos(t)

y=cos(t)+tsin(t)

## The Attempt at a Solution

dx/dt= cos(t)-(-tsin(t)) = cos(t)+tsint

dy/dt=-sin(t)+tcost

You're forgetting a minor detail. Recall the rules for differentiation, particularly products.

## 1. What is a derivative?

A derivative is a mathematical concept that represents the rate of change of one variable with respect to another variable. It is used to calculate the slope of a curve at a specific point.

## 2. Why is getting a derivative important?

Derivatives are important in many fields of science, from physics to economics. They allow us to understand how a system changes over time and make predictions about future behavior.

## 3. How do I calculate a derivative?

The most common method for calculating derivatives is using the rules of differentiation, such as the power rule or the product rule. These rules allow you to find the derivative of a function by following a set of steps.

## 4. What are some common mistakes when finding derivatives?

Some common mistakes when finding derivatives include forgetting to apply the chain rule, not simplifying the final answer, and making algebraic errors. It is important to double-check your work and practice regularly to avoid these mistakes.

## 5. What are some real-world applications of derivatives?

Derivatives have many real-world applications, such as predicting stock market trends, calculating the speed and acceleration of objects in motion, and optimizing manufacturing processes. They are also used in fields like engineering, biology, and medicine to model and understand complex systems.

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