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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 given function

Compute the derivative of the function

First, we simplify the given expression,

Then, we take the derivative,

# Compute the derivative of the given function

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 given function

Compute the derivative of the function

Using the chain rule we compute,

# Compute the derivative of the given function

Compute the derivative of the function

Using the chain rule we compute,

# Compute the derivative of the given function

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 given function

Compute the derivative of the function

Using the chain rule we compute,

# Compute the derivative of the given function

Compute the derivative of the function

Using the chain rule we compute,

# Compute the derivative of the given function

Compute the derivative of the function

Using the chain rule we compute,

# Compute the derivative of the given function

Compute the derivative of the function

Using the chain rule we compute,

where we used the trig identity in the second step.