(\partial ^3)/(\partial x\partial y\partial z)(e^{xyz^5})

解答

\frac{\partial ^{3}}{\partial x \partial y \partial z} (e^{x y z^{5}})

5 e^{x y z^{5}} x^{2} y^{2} z^{14} + 15 e^{x y z^{5}} x y z^{9} + 5 e^{x y z^{5}} z^{4}

求解步骤

\frac{\partial ^{3}}{\partial x \partial y \partial z} (e^{x y z^{5}})

\frac{\partial}{\partial x} (e^{x y z^{5}}) = e^{x y z^{5}} y z^{5}

= \frac{\partial ^{2}}{\partial y \partial z} (e^{x y z^{5}} y z^{5})

\frac{\partial}{\partial y} (e^{x y z^{5}} y z^{5}) = z^{5} (e^{x y z^{5}} x y z^{5} + e^{x y z^{5}})

= \frac{\partial}{\partial z} (z^{5} (e^{x y z^{5}} x y z^{5} + e^{x y z^{5}}))

\frac{\partial}{\partial z} (z^{5} (e^{x y z^{5}} x y z^{5} + e^{x y z^{5}})) = 5 e^{x y z^{5}} x^{2} y^{2} z^{14} + 15 e^{x y z^{5}} x y z^{9} + 5 e^{x y z^{5}} z^{4}

= 5 e^{x y z^{5}} x^{2} y^{2} z^{14} + 15 e^{x y z^{5}} x y z^{9} + 5 e^{x y z^{5}} z^{4}

in v erse l a pl a ce \frac{2}{( ( s - 4 ) s ( s + 1 ) )}

\int x^{2} + 4 x - 8 d x

\int_{- 1}^{- 2} (\frac{16 - x ^{3}}{x ^{3}}) d x

f (x) = x - 7

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