How do you find the derivative of #sinthetacsctheta#?

Answer 1

This is a question partly to see whether you remember your trigonometry and partly to teach you that it's OK to rewrite before differentiating..

#csc theta = 1/sin theta#, so

#sin theta csc theta = 1#,

and the derivative is #0#

If you want to do more trigonometry , then use the product rule to get

#(cos theta) (csc theta) + (sin theta) (-csc theta cot theta)#.

Now simplify to get

#cot theta - cot theta = 0#.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Cameron Alexander

To find the derivative of sin(theta) * csc(theta), use the product rule of differentiation. The derivative is sin(theta) * (-csc(theta) * cot(theta)) + cos(theta) * csc(theta).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

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.