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

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

Differentiate using the Exponential Rule which states that is where =.

To apply the Chain Rule, set as .

Differentiate using the Exponential Rule which states that is where =.

Replace all occurrences of with .

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

Simplify the expression.

Move to the left of .

Rewrite as .

Differentiate using the Power Rule which states that is where .

Multiply by .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

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

Differentiate using the Exponential Rule which states that is where =.

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

To apply the Chain Rule, set as .

Differentiate using the Exponential Rule which states that is where =.

Replace all occurrences of with .

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

Multiply.

Multiply by .

Multiply by .

Differentiate using the Power Rule which states that is where .

Multiply by .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Simplify the numerator.

Since both terms are perfect squares, factor using the difference of squares formula, where and .

Simplify.

Add and .

Add and .

Add and .

Apply the distributive property.

Subtract from .

Subtract from .

Subtract from .

Combine exponents.

Multiply by .

Multiply by by adding the exponents.

Move .

Use the power rule to combine exponents.

Add and .

Simplify .

Move the negative in front of the fraction.

Find the Derivative – d/dx y=(e^x+e^(-x))/(e^x-e^(-x))