(\partial)/(\partial x)(sqrt(x^5+y^7))

解答

\frac{\partial}{\partial x} (x^{5} + y^{7})

\frac{5 x ^{4}}{2 x ^{5} + y ^{7}}

求解步骤

\frac{\partial}{\partial x} (x^{5} + y^{7})

将

y

视为常数

使用连锁律:

\frac{1}{2 x ^{5} + y ^{7}} \frac{\partial}{\partial x} (x^{5} + y^{7})

= \frac{1}{2 x ^{5} + y ^{7}} \frac{\partial}{\partial x} (x^{5} + y^{7})

\frac{\partial}{\partial x} (x^{5} + y^{7}) = 5 x^{4}

= \frac{1}{2 x ^{5} + y ^{7}} \cdot 5 x^{4}

化简

\frac{1}{2 x ^{5} + y ^{7}} \cdot 5 x^{4} : \frac{5 x ^{4}}{2 x ^{5} + y ^{7}}

= \frac{5 x ^{4}}{2 x ^{5} + y ^{7}}

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

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