(\partial)/(\partial x)(e^{x/(b(x))})

解答

\frac{\partial}{\partial x} (e^{\frac{x}{b ( x )}})

\frac{e ^{\frac{x}{b ( x )}} ( b ( x ) - x \frac{\partial}{\partial x} ( b ( x ) ) )}{b ( x ) ^{2}}

求解步骤

\frac{\partial}{\partial x} (e^{\frac{x}{b ( x )}})

使用连锁律:

e^{\frac{x}{b ( x )}} \frac{\partial}{\partial x} (\frac{x}{b ( x )})

= e^{\frac{x}{b ( x )}} \frac{\partial}{\partial x} (\frac{x}{b ( x )})

\frac{\partial}{\partial x} (\frac{x}{b ( x )}) = \frac{b ( x ) - x \frac{\partial}{\partial x} ( b ( x ) )}{b ( x ) ^{2}}

= e^{\frac{x}{b ( x )}} \frac{b ( x ) - x \frac{\partial}{\partial x} ( b ( x ) )}{b ( x ) ^{2}}

分式相乘:

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

= \frac{e ^{\frac{x}{b ( x )}} ( b ( x ) - x \frac{\partial}{\partial x} ( b ( x ) ) )}{b ( x ) ^{2}}

t \to 0 lim (\frac{5}{1 + t})

y^{^{''}} - 3 y^{^{'}} = 18 t + 26 sin (2 t)

y^{^{''}} + 16 y = 32 sin (4 t)

\frac{d}{d x} (\frac{2}{3} x + \frac{4}{3 x ^{2}})

\frac{d}{d x} (f (x) \circ g (x))