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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

f (x) = x^{2} + x, at x = 1, x = 4

f (x) = x^{3} - 5 x^{2}

\int_{- 2}^{0} x^{2} e^{x^{3} + 8} d x

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

\int (x - 1) (x + 1) d x

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