Find the Derivative - d/dx y=tan(x)^2

Problem

d()/d(x)*tan2(x)

Solution

1. Identify the function as a composition of functions, specifically u2 where u=tan(x) which requires the use of the power rule and the chain rule.

2. Apply the power rule to the outer function by bringing the exponent 2 to the front and decreasing the power by 1

d(tan2(x))/d(x)=2*tan(x)⋅d(tan(x))/d(x)

3. Apply the derivative of the inner function, knowing that the derivative of tan(x) is sec2(x)

d(tan2(x))/d(x)=2*tan(x)*sec2(x)

Final Answer

d(tan2(x))/d(x)=2*tan(x)*sec2(x)

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