Differentiate using the Quotient Rule which states that is where and .

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

Since is constant with respect to , the derivative of with respect to is .

Add and .

The derivative of with respect to is .

Move to the left of .

Rewrite as .

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

Since is constant with respect to , the derivative of with respect to is .

Add and .

Since is constant with respect to , the derivative of with respect to is .

Multiply.

Multiply by .

Multiply by .

The derivative of with respect to is .

Move to the left of .

Rewrite as .

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify the numerator.

Simplify each term.

Multiply by .

Rewrite as .

Multiply .

Multiply by .

Multiply by .

Multiply .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Multiply by .

Rewrite as .

Multiply .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Combine the opposite terms in .

Subtract from .

Add and .

Subtract from .

Move the negative in front of the fraction.

Find the Derivative – d/dx y=(1+csc(x))/(1-csc(x))