# Find the Derivative f(x)=(sec(x))/(1+sec(x))

Differentiate using the Quotient Rule which states that is where and .
The derivative of with respect to is .
Differentiate.
By the Sum Rule, the derivative of with respect to is .
Since is constant with respect to , the derivative of with respect to is .
The derivative of with respect to is .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Simplify.
Apply the distributive property.
Apply the distributive property.
Simplify the numerator.
Simplify each term.
Multiply by .
Multiply .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.