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Riles246
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Homework Statement
d/dx (cos2x*sinx)
The Attempt at a Solution
Does this equal cos3x-2sin2x*cosx ?
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.
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.
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.
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.
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.