What is (\partial)/(\partial x)(sqrt(6-x^2+2y^2)) ?

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

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(\partial)/(\partial x)(sqrt(6-x^2+2y^2))

\frac{\partial}{\partial x} (6 - x^{2} + 2 y^{2})

- \frac{x}{6 - x ^{2} + 2 y ^{2}}

Solution steps

\frac{\partial}{\partial x} (6 - x^{2} + 2 y^{2})

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 6 - x ^{2} + 2 y ^{2}} \frac{\partial}{\partial x} (6 - x^{2} + 2 y^{2})

= \frac{1}{2 6 - x ^{2} + 2 y ^{2}} \frac{\partial}{\partial x} (6 - x^{2} + 2 y^{2})

\frac{\partial}{\partial x} (6 - x^{2} + 2 y^{2}) = - 2 x

= \frac{1}{2 6 - x ^{2} + 2 y ^{2}} (- 2 x)

Simplify

\frac{1}{2 6 - x ^{2} + 2 y ^{2}} (- 2 x) : - \frac{x}{6 - x ^{2} + 2 y ^{2}}

= - \frac{x}{6 - x ^{2} + 2 y ^{2}}

\frac{d}{d x} (A x^{2})

\int \frac{x + 3}{x ^{2} - 2 x - 3} d x

\int f (x + b) d x

x + 2

2 x^{3} - 4 x^{2}, at x = 1

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