函数y=x^2/cosx求dy

问题描述:

函数y=x^2/cosx求dy

dy=d(x^2/cosx)
=[cosxd(x^2)-x^2d(cosx)]/cos²x
=(2x*cosxdx+x²*sinxdx)/cos²x
=(2x*cosx+x²*sinx)dx/cos²x
=x(2secx+x*secx*tanx)dx

y=x²/cosx
dy=[cosx*2x - x²(-sinx)]/cos²x dx
=[x(2cosx+xsinx)/cos²x]dx
=x(2+xtanx)secx dx