# Find the Derivative – d/dx y=(arctan(5x))^2

Differentiate using the chain rule, which states that is where and .
To apply the Chain Rule, set as .
Differentiate using the Power Rule which states that is where .
Replace all occurrences of with .
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.
Factor out of .
Combine fractions.
Simplify the expression.
Apply the product rule to .
Raise to the power of .
Combine and .
Combine and .
Since is constant with respect to , the derivative of with respect to is .
Combine fractions.
Combine and .
Multiply by .
Differentiate using the Power Rule which states that is where .
Simplify the expression.
Multiply by .
Reorder terms.
Find the Derivative – d/dx y=(arctan(5x))^2