Question

How do I find the derivative of `y=arctan(cos θ)`?

Answer 1

`y'=-(sintheta)/(cos^(2)theta+1)`

`y=arctan(costheta)`

Applying the chain rule:

`y'=(1)/(cos^(2)theta+1)xx(d[costheta])/("d"theta)`

`=(-sintheta)/(cos^(2)theta+1)`

`=-(sintheta)/(cos^(2)theta+1)`