How Do You Apply the Chain Rule to Derivatives of Trigonometric Functions?

In summary: It is an important rule for finding derivatives of composite functions, which is what (cos)^3(t) and (sin)^3(t) are. You can use the Chain Rule to find the derivatives of these functions. In summary, to find the derivatives of (cos)^3(t) and (sin)^3(t), you can use the Chain Rule, which is an important rule for finding derivatives of composite functions.
  • #1
jimbo71
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Homework Statement


How would I find d/dt of (cos)^3(t).
How would I find d/dt of (sin)^3(t)


Homework Equations





The Attempt at a Solution

 
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  • #2
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  • #3
I have no idea to do it or I would have show my attempt. All I know is the derivatives of cosx is -sinx and sinx is cosx
 
  • #4
Haven't you learned about the Chain Rule?
 

Related to How Do You Apply the Chain Rule to Derivatives of Trigonometric Functions?

1. What is the derivative of a trigonometric function?

The derivative of a trigonometric function is the rate of change of the function at a particular point. It represents the slope of the tangent line to the function at that point.

2. How do you find the derivative of a trigonometric function?

The derivative of a trigonometric function can be found using the standard rules of differentiation, such as the power rule, product rule, and chain rule. It is important to remember the derivative formulas for each trigonometric function, such as sin(x), cos(x), tan(x), etc.

3. What are the common trigonometric functions?

The most commonly used trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc). These functions are used to describe the relationships between the sides and angles of a right triangle.

4. What is the purpose of finding the derivative of a trigonometric function?

The derivative of a trigonometric function is used to analyze the behavior of the function and its rate of change. It is also used to solve real-world problems involving trigonometric functions, such as finding the maximum or minimum values of a function.

5. How is the derivative of a trigonometric function related to its graph?

The derivative of a trigonometric function is related to its graph by the slope of the tangent line at each point on the graph. The derivative can tell us about the increasing or decreasing behavior of the function and the concavity of the graph.

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