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Consider the function We could make a graph of the slope: slope Now we connect the dots! The resulting curve is a cosine curve. 2.3 Derivatives of Trigonometric Functions

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Proof

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2.3 Derivatives of Trigonometric Functions = 0 = 1

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2.3 Derivatives of Trigonometric Functions Find the derivative of cos x

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2.3 Derivatives of Trigonometric Functions = 0 = 1

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We can find the derivative of tangent x by using the quotient rule. 2.3 Derivatives of Trigonometric Functions = = = = =

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Derivatives of the remaining trig functions can be determined the same way. 2.3 Derivatives of Trigonometric Functions

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Chain Rule: 2.4 Chain Rule Let h(x) = f(g(x)) (also known as ) Then h(x) = (f(g(x)) =

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Here is a faster way to find the derivative: Differentiate the outside function... …then the inside function 2.4 Chain Rule

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The chain rule can be used more than once. (Thats what makes the chain in the chain rule!) 2.4 Chain Rule = = = = =

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Derivative formulas include the chain rule! etcetera… 2.4 Chain Rule

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Find

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Product rule: Notice that this is not just the product of two derivatives. This is sometimes memorized as:

Product rule: Notice that this is not just the product of two derivatives. This is sometimes memorized as:

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