What is (\partial)/(\partial x)(sqrt(5-y^3-x^7)) ?

The answer to (\partial)/(\partial x)(sqrt(5-y^3-x^7)) is -(7x^6)/(2sqrt(5-y^3-x^7))

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(\partial)/(\partial x)(sqrt(5-y^3-x^7))

\frac{\partial}{\partial x} (5 - y^{3} - x^{7})

- \frac{7 x ^{6}}{2 5 - y ^{3} - x ^{7}}

Solution steps

\frac{\partial}{\partial x} (5 - y^{3} - x^{7})

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 5 - y ^{3} - x ^{7}} \frac{\partial}{\partial x} (5 - y^{3} - x^{7})

= \frac{1}{2 5 - y ^{3} - x ^{7}} \frac{\partial}{\partial x} (5 - y^{3} - x^{7})

\frac{\partial}{\partial x} (5 - y^{3} - x^{7}) = - 7 x^{6}

= \frac{1}{2 5 - y ^{3} - x ^{7}} (- 7 x^{6})

Simplify

\frac{1}{2 5 - y ^{3} - x ^{7}} (- 7 x^{6}) : - \frac{7 x ^{6}}{2 5 - y ^{3} - x ^{7}}

= - \frac{7 x ^{6}}{2 5 - y ^{3} - x ^{7}}

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What is (\partial)/(\partial x)(sqrt(5-y^3-x^7)) ?
The answer to (\partial)/(\partial x)(sqrt(5-y^3-x^7)) is -(7x^6)/(2sqrt(5-y^3-x^7))