f（x）=sin[2^x-2^(1/x)]f'(x)=cos[2^x-2^(1/x)]* [2^x-2^(1/x)]'=[2^x*ln2-2^(1/x)*ln2*(1/x)']*cos[2^x-2^(1/x)]=[2^x+1/x²*2^(1/x)]ln2*cos[2^x-2^(1/x)]