# What is the derivative of #y=ln(cos^2ɵ)#?

Assuming that we want

Method 1 Leave it as is and use the chain rule twice:

Use the chain rule: (less detail this time)

So

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To find the derivative of ( y = \ln(\cos^2\theta) ), you can use the chain rule. The derivative is:

[ \frac{dy}{d\theta} = \frac{1}{\cos^2\theta} \cdot (-2\cos\theta \cdot (-\sin\theta)) ]

Simplified, this becomes:

[ \frac{dy}{d\theta} = \frac{2\sin\theta}{\cos\theta} ]

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The derivative of ( y = \ln(\cos^2 \theta) ) with respect to ( \theta ) is ( \frac{d}{d\theta}[\ln(\cos^2 \theta)] = \frac{-2\sin \theta}{\cos^2 \theta} ).

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