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

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 =.
Differentiate using the chain rule, which states that is where and .
To apply the Chain Rule, set as .
Differentiate using the Exponential Rule which states that is where =.
Replace all occurrences of with .
Differentiate.
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.
Differentiate using the Sum Rule.
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 .
Differentiate using the chain rule, which states that is where and .
To apply the Chain Rule, set as .
Differentiate using the Exponential Rule which states that is where =.
Replace all occurrences of with .
Differentiate.
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.
Simplify.
Simplify the numerator.
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Simplify.
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.