高二数学导数基础tanx+cotx求导,答案变形为-4cos2x/sin2x^2;x^2lnx+1/logaX(a>0,a不等于1,x>0)求导,答案变形为2xlnx+x-lna/xlnx^2.急需,谢~~

Question

高二数学导数基础
tanx+cotx求导,答案变形为-4cos2x/sin2x^2;x^2lnx+1/logaX(a>0,a不等于1,x>0)求导,答案变形为2xlnx+x-lna/xlnx^2.急需,谢~~

Answer 1

(tanx+cotx)'
=sec²x-csc²x
=(sin²x-cos²x)/sin²xcos²x
=(1-2cos²x)/sin²xcos²x
=2(1-cos²x)/sin²xcos²x - 1/sin²xcos²x
=8cos2x/sin²2x - 2/sin²2x
=2(4cos2x - 1)/sin²2x
(x^2lnx+1/logaX)'
=(x²lnx+lna/lnx)'
=2xlnx+x+lna(-1/ln²x)/x
=2xlnx+x-lna/xln²x