Derivative of exponential functions: x/(e^(2x))?

It's easy enough to simplify g(x) to show that it's really the same as f(x), but this obviously isn't what they're asking for. You have to explicitly take the derivative of each function, then simplify to show they're the same. The derivative of ln(tan(x)) is 1 / tan(x) times the derivative of tan(x), which gives you (1 / tan(x)) sec^2(x) sec^2(x) / tan(x) Likewise, g ' (x) is (1/sin(x))cos(x) - (1/cos(x))(-sin(x)).

Simplifying g ' (x) gives you cos(x)/sin(x) + sin(x)/cos(x) cos^2(x)/sin(x)cos(x) + sin^2(x)/sin(x)cos(x) cos^2(x) + sin^2(x) / sin(x)cos(x) 1 / sin(x)cos(x) (1 / sin(x)) sec(x) (cos(x) / sin(x)) sec^2(x) sec^2(x) / tan(x).

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