y=(1+x²)arctanx dy/dx = 2xarctanx + (1+x²)×[1/(1+x²)] = 2xarctanx + 1 d²y/dx²= 2arctanx + 2x/(1+x²) 链式求导的一般方法: y = uvwpqr dy/dx = (du/dx)vwpqr + u(dv/dx)wpqr + uv(dw/dx)pqr + uvw(dp/dx)qr + uvwp(dq/dx)r + uvwpq(dr/dx)
y=(1+x²)arctanx dy/dx = 2xarctanx + (1+x²)×[1/(1+x²)] = 2xarctanx + 1 d²y/dx²= 2arctanx + 2x/(1+x²) 链式求导的一般方法: y = uvwpqr dy/dx = (du/dx)vwpqr + u(dv/dx)wpqr + uv(dw/dx)pqr + uvw(dp/dx)qr + uvwp(dq/dx)r + uvwpq(dr/dx)