# How do you find the derivative of # y = ln(secx)#?

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See below

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In order to differentiate this function, we must use the chain rule:

Informally, this means that if we have to derivate a composite function,

The function to derivate is

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We can also rewrite this using logarithm rules:

#y=ln(secx)=ln(1/cosx)=ln((cosx)^-1)=-ln(cosx)#

The derivative of

Thus,

#dy/dx=-1/cosx*d/dxcosx#

The derivative of

#dy/dx=-1/cosx(-sinx)=sinx/cosx=tanx#

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