# Calculus - find dy/dt thank you

• laker_gurl3
In summary, the conversation is about finding the derivative of dy/dt = x^2 Tanx / sec x and the answer in the book was x(xcosx + 2sinx). The person is asking for help and someone responds with the steps to find the derivative.
laker_gurl3
calculus -.. find dy/dt...thank you..:(

can someone please help me out with this question...i did it all sorts of way,quotient rule, product rule..etc.. but i can never match the answer in the book..i just want to know if u did..

find dy/dt = x^2 Tanx / sec x

The answer in the book was
x(xcosx + 2sinx)

lemmi know how you did it with a couple steps! thanks soo mcuh

Do you mean find

$$\frac{d}{dx} \frac{x^2 \tan{x}}{\sec{x}}$$

?

If so, here:

$$\frac{x^2 \tan{x}}{\sec{x}} = x^2\tan{x}\cos{x} = x^2 \frac{\sin{x}}{\cos{x}}\cos{x} = x^2 \sin{x}$$

I'm sure you can take the derivative from there~

Damn you Data!

got to be quick

## 1. What is the meaning of dy/dt in calculus?

The notation dy/dt in calculus represents the derivative of a function y with respect to the independent variable t. It measures the rate of change of y with respect to t, or in other words, how quickly y is changing at a specific point in time.

## 2. How do I find dy/dt in calculus?

To find dy/dt, you need to take the derivative of the function y with respect to t. This can be done using the rules of differentiation, such as the power rule, product rule, and chain rule. Once you have the derivative, you can substitute in the specific value of t to find the instantaneous rate of change at that point.

## 3. What is the significance of dy/dt in real-world applications?

In real-world applications, dy/dt represents the instantaneous rate of change of a quantity. This is useful in fields such as physics and engineering, where it can be used to model and predict the behavior of systems that are constantly changing over time.

## 4. Can dy/dt be negative in calculus?

Yes, dy/dt can be negative in calculus. This indicates that the function y is decreasing at a specific point in time. It is important to note that the sign of dy/dt does not necessarily reflect the overall behavior of the function, as it may be increasing or decreasing at different points.

## 5. How can I use dy/dt to solve related rates problems?

Related rates problems involve finding the rate of change of one quantity with respect to another. In these problems, dy/dt can be used as a tool to relate the rates of change of the two quantities. By setting up and solving a related rates equation using dy/dt, you can find the desired rate of change.

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