Chain Rule Practice: d/dx (cos2xsinx) = cos3x-2sin2xcosx?

Thread starter Riles246
Start date Sep 5, 2008
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Chain Chain rule

In summary, the chain rule in calculus is a method for finding the derivative of a composite function. To apply it, you need to identify the inner and outer functions and multiply the derivative of the outer function by the derivative of the inner function. The derivative of cos(x) is -sin(x), and the derivative of sin(x) is cos(x). To use the chain rule to find the derivative of cos2x*sinx, you rewrite it as a composite function and then take the derivative of the outer function, evaluate it at the inner function, and multiply it by the derivative of the inner function.

Sep 5, 2008

Riles246

Homework Statement

d/dx (cos²x*sinx)

The Attempt at a Solution

Does this equal cos³x-2sin²x*cosx ?

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Sep 5, 2008

Dick

Science Advisor

Homework Helper

It sure does.

FAQ: Chain Rule Practice: d/dx (cos2xsinx) = cos3x-2sin2xcosx?

What is the chain rule in calculus?

The chain rule in calculus is a method for finding the derivative of a composite function. It states that the derivative of a composite function is equal to the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function.

How do you apply the chain rule?

To apply the chain rule, you first need to identify the inner and outer functions in the composite function. Then, you take the derivative of the outer function and evaluate it at the inner function. Finally, you multiply this result by the derivative of the inner function.

What is the derivative of cos(x)?

The derivative of cos(x) is -sin(x). This can be found by using the chain rule, where the outer function is cos(x) and the inner function is x.

What is the derivative of sin(x)?

The derivative of sin(x) is cos(x). This can also be found using the chain rule, with the outer function being sin(x) and the inner function being x.

How do you use the chain rule to find the derivative of cos2x*sinx?

To find the derivative of cos2x*sinx, you first need to rewrite it as a composite function: (cos2x) * sinx. Then, you can use the chain rule by taking the derivative of the outer function (cos2x) and evaluating it at the inner function (sinx), which gives -2sin2x. Finally, you multiply this by the derivative of the inner function (cosx), giving a final result of -2sin2x*cosx.