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

The derivative of with respect to is .

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 .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

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.

Add and .

Combine the opposite terms in .

Subtract from .

Add and .

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