Compute the derivative of the function

Using the chain rule,

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Stumbling Robot

A Fraction of a Dot
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Tag: Chain Rule

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Compute the derivative of the given function

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Compute the derivative of the given function

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Compute the derivative of the given function

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Compute the derivative of the given function

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Compute the derivative of the given function

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Compute the derivative of the given function

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Compute the derivative of the given function

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Compute the derivative of the given function

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Compute the derivative of the given function

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Compute the derivative of the given function

Compute the derivative of the function

Using the chain rule,

Compute the derivative of the function

First, we simplify the given expression,

Then, we take the derivative,

Compute the derivative of the function

We recall the derivatives and . (We proved these in this exercise, found in Apostol Section 4.6, Exercise #25.) Then, we use the chain rule to compute

The second to last equality follows from the trig identity since,

Implies,

Compute the derivative of the function

Using the chain rule we compute,

Compute the derivative of the function

Using the chain rule we compute,

Compute the derivative of the function

Using the chain rule we compute,

The final equality follows from the identity since

Compute the derivative of the function

Using the chain rule we compute,

Compute the derivative of the function

Using the chain rule we compute,

Compute the derivative of the function

Using the chain rule we compute,

Compute the derivative of the function

Using the chain rule we compute,

where we used the trig identity in the second step.