What is (\partial)/(\partial x)(sqrt(9-x^3-y^5)) ?

The answer to (\partial)/(\partial x)(sqrt(9-x^3-y^5)) is -(3x^2)/(2sqrt(9-x^3-y^5))

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(\partial)/(\partial x)(sqrt(9-x^3-y^5))

\frac{\partial}{\partial x} (9 - x^{3} - y^{5})

- \frac{3 x ^{2}}{2 9 - x ^{3} - y ^{5}}

Solution steps

\frac{\partial}{\partial x} (9 - x^{3} - y^{5})

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 9 - x ^{3} - y ^{5}} \frac{\partial}{\partial x} (9 - x^{3} - y^{5})

= \frac{1}{2 9 - x ^{3} - y ^{5}} \frac{\partial}{\partial x} (9 - x^{3} - y^{5})

\frac{\partial}{\partial x} (9 - x^{3} - y^{5}) = - 3 x^{2}

= \frac{1}{2 9 - x ^{3} - y ^{5}} (- 3 x^{2})

Simplify

\frac{1}{2 9 - x ^{3} - y ^{5}} (- 3 x^{2}) : - \frac{3 x ^{2}}{2 9 - x ^{3} - y ^{5}}

= - \frac{3 x ^{2}}{2 9 - x ^{3} - y ^{5}}

\frac{d}{d x} (6^{4 - 3 x})

\frac{d}{d x} (\frac{x}{x ^{2} + 49})

\int x^{- \frac{1}{7}} d x

\frac{1}{x + 4}

\int \frac{x ^{5}}{x ^{6} + 1} d x

What is (\partial)/(\partial x)(sqrt(9-x^3-y^5)) ?
The answer to (\partial)/(\partial x)(sqrt(9-x^3-y^5)) is -(3x^2)/(2sqrt(9-x^3-y^5))