derivative of ce^{y/x}

解答

\frac{d}{d x} (c e^{\frac{y}{x}})

\frac{c e ^{\frac{y}{x}} ( x \frac{d y}{d x} - y )}{x ^{2}}

求解步骤

\frac{d}{d x} (c e^{\frac{y}{x}})

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= c \frac{d}{d x} (e^{\frac{y}{x}})

使用连锁律:

e^{\frac{y}{x}} \frac{d}{d x} (\frac{y}{x})

= e^{\frac{y}{x}} \frac{d}{d x} (\frac{y}{x})

\frac{d}{d x} (\frac{y}{x}) = \frac{x \frac{d y}{d x} - y}{x ^{2}}

= c e^{\frac{y}{x}} \frac{x \frac{d y}{d x} - y}{x ^{2}}

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{c e ^{\frac{y}{x}} ( x \frac{d y}{d x} - y )}{x ^{2}}

\frac{\partial}{\partial x} (x + y + ∣ x ∣^{3} y^{2})

\frac{d}{d x} (5 x^{2 π})

d er i v a t i v e (\frac{10 - ( 2 )}{( x )}) \cdot (\frac{3 + ( 1 )}{( x )})

(\frac{1}{1 + e ^{x}})^{^{'}}

d er i v a t i v e - 3 x x + 1