How do you differentiate #(ln(2x) )/ (cos2x)# using the quotient rule?
with:
Applying Quotient Rule
then:
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To differentiate (ln(2x)) / (cos(2x)) using the quotient rule, you first find the derivative of the numerator and denominator separately.
The derivative of ln(2x) with respect to x is (1/(2x)) * (d/dx)(2x), which simplifies to 1/x.
The derivative of cos(2x) with respect to x is -2sin(2x).
Then, apply the quotient rule:
[f'(x)g(x) - f(x)g'(x)] / [g(x)]^2
= [(1/x)(cos(2x)) - (ln(2x))(-2sin(2x))] / [cos(2x)]^2
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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