# Find the Derivative – d/dx y=(sec(2x))/(1+tan(2x))

Differentiate using the Quotient Rule which states that is where and .
Differentiate using the chain rule, which states that is where and .
To apply the Chain Rule, set as .
The derivative of with respect to is .
Replace all occurrences of with .
Differentiate.
Since is constant with respect to , the derivative of with respect to is .
Move to the left of .
Differentiate using the Power Rule which states that is where .
Multiply by .
By the Sum Rule, the derivative of with respect to is .
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 .
The derivative of with respect to is .
Replace all occurrences of with .
Raise to the power of .
Use the power rule to combine exponents.
Since is constant with respect to , the derivative of with respect to is .
Multiply by .
Differentiate using the Power Rule which states that is where .
Multiply by .
Simplify.
Apply the distributive property.
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.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Reorder and .
Factor out of .
Factor out of .
Factor out of .
Apply pythagorean identity.
Multiply by .
Apply the distributive property.
Multiply by .
Find the Derivative – d/dx y=(sec(2x))/(1+tan(2x))

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