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

Problem

d(tan(2*x))/d(x)

Solution

1. Identify the outer function as tan(u) and the inner function as u=2*x

2. Apply the chain rule, which states that (d(ƒ)*(g(x)))/d(x)=ƒ^′*(g(x))⋅g(x)^′

3. Differentiate the outer function tan(u) with respect to u to get sec^2(u)

4. Differentiate the inner function 2*x with respect to x to get 2

5. Multiply the results together and substitute 2*x back for u

Final Answer

d(tan(2*x))/d(x)=2*sec^2(2*x)

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