This example shows how to calculate the derivative of the sine function using a Taylor series.
Start with the taylor series definition of the sine function[1].
Take the derivative of both sides of the equation.
From the summation property of derivatives, we can apply the power rule to each of the expressions on the right-hand side of the equation.
Simplify the factorial operator in the denominator.
This gives us the taylor series definition of the cosine function[2] which we can substitute in for on the right-hand side.
The derivative of is .
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Derive Sine Function (Taylor Series) Example
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Derive Cosine Function (Taylor Series) Example