(\partial)/(\partial x)(ln(x^6-y^6))

解答

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

\frac{6 x ^{5}}{x ^{6} - y ^{6}}

求解步骤

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

将

y

视为常数

使用连锁律:

\frac{1}{x ^{6} - y ^{6}} \frac{\partial}{\partial x} (x^{6} - y^{6})

= \frac{1}{x ^{6} - y ^{6}} \frac{\partial}{\partial x} (x^{6} - y^{6})

\frac{\partial}{\partial x} (x^{6} - y^{6}) = 6 x^{5}

= \frac{1}{x ^{6} - y ^{6}} \cdot 6 x^{5}

化简

\frac{1}{x ^{6} - y ^{6}} \cdot 6 x^{5} : \frac{6 x ^{5}}{x ^{6} - y ^{6}}

= \frac{6 x ^{5}}{x ^{6} - y ^{6}}

\frac{d}{d M} (\frac{2 π r ^{\frac{3}{2}}}{GM})

\frac{d}{d x} (x^{3} - \frac{4}{x})

t an g e n t y = \frac{2 x}{( x + 1 ) ^{2}}, (0, 0)

y^{^{'}} + (cot (x)) y = sin^{2} (x)

d er i v a t i v e \frac{ln ( x )}{5 x ^{2}}