Question

Differentiate the function K(x)=2^tanx

Answer 1

2 to the power of tanx? This seems like a weird function but I suggest you use the chain rule:\[\frac{ da }{ db }=\frac{ da }{ dc } \times \frac{ dc }{ db }\]

Answer 2

Let m(x) = 2^x and n(x) = tan(x)
Thus find the derivative of m(n(x)), w/c is
m'(n(x)) * n"(x)
Therefore the final answer will be\[\ln(2){\times}2^{\tan(x)}\sec^{2}(x)\]

Answer 3

Yup, that seems right. Incidentally, you can check your answer by typing the function into:
http://www.wolframalpha.com/
It can differentiate things for you.