罗尔定理

f(x)f′(x)f(x)f'(x)的原函数辅助函数F(x)=f2(x)F(x)=f^2(x)

[f′(x)]2+f(x)f′′(x)[f'(x)]^2+f(x)f''(x)的原函数辅助函数F(x)=f(x)f′(x)F(x)=f(x)f'(x)

f′(x)+f(x)ϕ′(x)f'(x)+f(x)\phi'(x)的原函数辅助函数F(x)=f(x)eϕ(x)F(x)=f(x)e^{\phi(x)}

f′(x)+f(x)f'(x)+f(x)的原函数辅助函数F(x)=f(x)exF(x)=f(x)e^x

f′(x)−f(x)f'(x)-f(x)的原函数辅助函数F(x)=f(x)e−xF(x)=f(x)e^{-x}

f′(x)+kf(x)f'(x)+kf(x)的原函数辅助函数F(x)=f(x)ekxF(x)=f(x)e^{kx}