(\partial)/(\partial x)(x^{0.25}y^{0.5})

解答

\frac{\partial}{\partial x} (x^{0.25} y^{0.5})

\frac{0.25 y ^{\frac{1}{2}}}{x ^{0.75}}

求解步骤

\frac{\partial}{\partial x} (x^{0.25} y^{0.5})

将

y

视为常数

将常数提出:

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

= y^{0.5} \frac{\partial}{\partial x} (x^{0.25})

使用幂法则:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= y^{0.5} \cdot 0.25 x^{0.25 - 1}

化简

y^{\frac{1}{2}} \cdot 0.25 x^{0.25 - 1} : \frac{0.25 y ^{\frac{1}{2}}}{x ^{0.75}}

= \frac{0.25 y ^{\frac{1}{2}}}{x ^{0.75}}

\frac{d y}{d x} = x - 3

\int 7 tan^{3} (x) sec^{3} (x) d x

\int x (2 x + 1)^{2} d x

t an g e n t f (x) = x^{2} + 4, (4, 20)

x \to 2 - lim (e^{\frac{1}{x - 2}})