What is (\partial)/(\partial x)(sqrt(5-x^2+3y^2)) ?

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

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(\partial)/(\partial x)(sqrt(5-x^2+3y^2))

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

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