(\partial)/(\partial x)(sqrt(7-x^3-y^7))

解答

\frac{\partial}{\partial x} (7 - x^{3} - y^{7})

- \frac{3 x ^{2}}{2 7 - x ^{3} - y ^{7}}

求解步骤

\frac{\partial}{\partial x} (7 - x^{3} - y^{7})

将

y

视为常数

使用连锁律:

\frac{1}{2 7 - x ^{3} - y ^{7}} \frac{\partial}{\partial x} (7 - x^{3} - y^{7})

= \frac{1}{2 7 - x ^{3} - y ^{7}} \frac{\partial}{\partial x} (7 - x^{3} - y^{7})

\frac{\partial}{\partial x} (7 - x^{3} - y^{7}) = - 3 x^{2}

= \frac{1}{2 7 - x ^{3} - y ^{7}} (- 3 x^{2})

化简

\frac{1}{2 7 - x ^{3} - y ^{7}} (- 3 x^{2}) : - \frac{3 x ^{2}}{2 7 - x ^{3} - y ^{7}}

= - \frac{3 x ^{2}}{2 7 - x ^{3} - y ^{7}}

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