Question

导数y=(2lnx+x³)/(3lnx+x²）的解法

Answer 1

y=(2lnx+x³)/(3lnx+x²)

用导数商法则

dy/dx=[(3lnx+x²)(2lnx+x³)'-(2lnx+x³)(3lnx+x²)']/(3lnx+x²)²

=[(3lnx+x²)(2/x+3x²)-(2lnx+x³)(3/x+2x)]/(3lnx+x²)²

=(3x^4+9x²lnx+2x+6lnx/x-2x^4-3x²-4xlnx-6lnx/x)/(3lnx+x²)²

=x(x³-3x+9xlnx-4lnx+2)/(3lnx+x²)²