(\partial)/(\partial x)(e^{sqrt(|xyz|)})

解答

\frac{\partial}{\partial x} (e^{∣ x yz ∣})

\frac{e ^{∣ x ∣ ∣ y ∣ ∣ z ∣} x ∣ y ∣ ∣ z ∣}{2 ∣ x ∣ ∣ x ∣}

求解步骤

\frac{\partial}{\partial x} (e^{∣ x yz ∣})

化简

e^{∣ x yz ∣} : e^{∣ x ∣ ∣ y ∣ ∣ z ∣}

= \frac{\partial}{\partial x} (e^{∣ x ∣ ∣ y ∣ ∣ z ∣})

将

y, z

视为常数

使用连锁律:

e^{∣ x ∣ ∣ y ∣ ∣ z ∣} \frac{\partial}{\partial x} (∣ x ∣ ∣ y ∣ ∣ z ∣)

= e^{∣ x ∣ ∣ y ∣ ∣ z ∣} \frac{\partial}{\partial x} (∣ x ∣ ∣ y ∣ ∣ z ∣)

\frac{\partial}{\partial x} (∣ x ∣ ∣ y ∣ ∣ z ∣) = \frac{x ∣ y ∣ ∣ z ∣}{2 ∣ x ∣ ∣ x ∣}

= e^{∣ x ∣ ∣ y ∣ ∣ z ∣} \frac{x ∣ y ∣ ∣ z ∣}{2 ∣ x ∣ ∣ x ∣}

分式相乘:

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

= \frac{e ^{∣ x ∣ ∣ y ∣ ∣ z ∣} x ∣ y ∣ ∣ z ∣}{2 ∣ x ∣ ∣ x ∣}

\frac{\partial}{\partial y} (y^{2} - 2 x y + 6 x)

\int_{0}^{1} \frac{x}{e ^{x^{2}}} d x

\frac{\partial}{\partial y} (\frac{a x}{y ^{2}})

\int \frac{1}{cos ( 8 x )} d x

\int_{0}^{2} 6 x (2 - x) d x