Differentiate the function. ) = ln(sin2

[Pages:1]Stewart Calculus 8e: Section 3.6 - Exercise 4

Exercise 4

Differentiate the function.

f (x) = ln(sin2 x)

Solution

Take the derivative of the function using the chain rule.

f (x) = d [ln(sin2 x)] dx

=

1 sin2

x

?

d (sin2 dx

x)

1

d

=

sin2

x

?

(2 sin x)

?

(sin x) dx

1 = sin2 x ? (2 sin x) ? (cos x)

2 sin x cos x = sin2 x

2 cos x =

sin x

= 2 cot x

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