3、设f(x)二阶可导,求y=f(根号(x^2+1))对x的一阶导数和二阶导数
∫1/x^2*sin(2/x+3)dx
=-∫sin(2/x +3)d(1/x)
=-1/2 ∫sin(2/x +3)d(2/x+3)
=1/2 cos(2/x +3)+c
z=6-z/2,
2z=12-z
3z=12
z=4
x²+y²=2
体积=∫∫ (6-x²-y²-2x²-2y²)dxdy
=∫∫(6-3x²-3y²)dxdy
=∫∫(6-3p²)pdpdθ
=∫(0,2π)dθ∫(0,根号2)(6p-3p³)dp
=2π (3p²-3/4p^4)|(0,根号2)
=2π (3×2-3/4 ×2²)
=2π×3
=6π
y'=f'(√(x²+1))· 2x/[2√(x²+1)]
=x/√(x²+1) ·f'(√(x²+1))
y''=(√(x²+1)-x·x/√(x²+1))/√(x²+1)² ·f'(√(x²+1))+x/√(x²+1) f''(√(x²+1))·x/√(x²+1)
=1/(x²+1)^(3/2) f'(√(x²+1)) +x²/(x²+1) f''(√(x²+1))
1年前