y = cos(cot x)

Question

Calculus Question Find the derivative of each function.

Answer 1

We use the chain rule for this one.  Notice that cotx is the argument of cosine.  So we have to evaluate cotx first, then find the cosine of that result.

 

The formula for chain rule is derivative of the inner function times the derivative of the outer function evaluated inside.

 

 

First step:  Derive the inner function, which is cotx.

 

-csc²x

 

 

Second step:  Derive the outer function evaluated inside.  This function is cos(x).

 

y' = -csc²x*(sinx(cotx))

Answer 2

y = cos (cot x)

 

y' = -sin (cot x) * -csc² x = csc² x * sin (cot x)

 

When you have a trigonometric function, you must take a derivative of the function first & then multiply it by the derivative of the angle.