Differentiate both sides of the equation.

The derivative of with respect to is .

Differentiate using the chain rule, which states that is where and .

To apply the Chain Rule, set as .

Differentiate using the Power Rule which states that is where .

Replace all occurrences of with .

By the Sum Rule, the derivative of with respect to is .

The derivative of with respect to is .

The derivative of with respect to is .

Reform the equation by setting the left side equal to the right side.

Rewrite the expression using the negative exponent rule .

Apply the distributive property.

Multiply .

Multiply by .

Multiply by .

Combine and .

Combine and .

Multiply .

Multiply by .

Multiply by .

Combine and .

Replace with .

Find dy/dx y=(csc(x)+cot(x))^-1