# How do you find the derivative of #log(sin^2(x))#?

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To find the derivative of log(sin^2(x)), you can use the chain rule along with the fact that the derivative of log(u) with respect to u is 1/u.

Let y = log(sin^2(x)). Then, y = log(u) where u = sin^2(x).

Now, applying the chain rule:

dy/dx = (1/u) * du/dx = (1/sin^2(x)) * d/dx(sin^2(x)) = (1/sin^2(x)) * (2sin(x) * cos(x)) = 2cot(x)

So, the derivative of log(sin^2(x)) with respect to x is 2cot(x).

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To find the derivative of ( \log(\sin^2(x)) ), you can apply the chain rule. The chain rule states that if you have a function ( f(g(x)) ), then its derivative is ( f'(g(x)) \cdot g'(x) ). In this case, ( f(x) = \log(x) ) and ( g(x) = \sin^2(x) ).

The derivative of ( \log(x) ) with respect to ( x ) is ( \frac{1}{x} ). So, the derivative of ( \log(\sin^2(x)) ) will be ( \frac{1}{\sin^2(x)} ) multiplied by the derivative of ( \sin^2(x) ) with respect to ( x ).

To find the derivative of ( \sin^2(x) ), you can use the chain rule again. The derivative of ( \sin^2(x) ) with respect to ( x ) is ( 2\sin(x)\cos(x) ).

Therefore, putting it all together, the derivative of ( \log(\sin^2(x)) ) with respect to ( x ) is ( \frac{1}{\sin^2(x)} \cdot 2\sin(x)\cos(x) ), which simplifies to ( \frac{2\sin(x)\cos(x)}{\sin^2(x)} ).

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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.

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