derivative of (2x/(3y^2))

解答

\frac{d}{d x} (\frac{2 x}{3 y ^{2}})

\frac{2 ( y - 2 x \frac{d y}{d x} )}{3 y ^{3}}

求解步骤

\frac{d}{d x} (\frac{2 x}{3 y ^{2}})

将常数提出:

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

= \frac{2}{3} \frac{d}{d x} (\frac{x}{y ^{2}})

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{2}{3} \cdot \frac{\frac{d x}{d x} y ^{2} - \frac{d}{d x} ( y ^{2} ) x}{( y ^{2} ) ^{2}}

\frac{d x}{d x} = 1

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

= \frac{2}{3} \cdot \frac{1 \cdot y ^{2} - 2 y \frac{d y}{d x} x}{( y ^{2} ) ^{2}}

化简

\frac{2}{3} \cdot \frac{1 \cdot y ^{2} - 2 y \frac{d y}{d x} x}{( y ^{2} ) ^{2}} : \frac{2 ( y - 2 x \frac{d y}{d x} )}{3 y ^{3}}

= \frac{2 ( y - 2 x \frac{d y}{d x} )}{3 y ^{3}}

\int cos^{3} (1) d x

d er i v a t i v e f (x) = (3 x + 2) (4 x^{2} + 3)

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

\frac{d}{d x} (sec (\frac{x}{2}))

\int e^{x + y + z} d x