What is (\partial)/(\partial x)(sqrt(8+x^2-2y^2)) ?

The answer to (\partial)/(\partial x)(sqrt(8+x^2-2y^2)) is x/(sqrt(8+x^2-2y^2))

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(\partial)/(\partial x)(sqrt(8+x^2-2y^2))

\frac{\partial}{\partial x} (8 + x^{2} - 2 y^{2})

\frac{x}{8 + x ^{2} - 2 y ^{2}}

Solution steps

\frac{\partial}{\partial x} (8 + x^{2} - 2 y^{2})

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 8 + x ^{2} - 2 y ^{2}} \frac{\partial}{\partial x} (8 + x^{2} - 2 y^{2})

= \frac{1}{2 8 + x ^{2} - 2 y ^{2}} \frac{\partial}{\partial x} (8 + x^{2} - 2 y^{2})

\frac{\partial}{\partial x} (8 + x^{2} - 2 y^{2}) = 2 x

= \frac{1}{2 8 + x ^{2} - 2 y ^{2}} \cdot 2 x

Simplify

\frac{1}{2 8 + x ^{2} - 2 y ^{2}} \cdot 2 x : \frac{x}{8 + x ^{2} - 2 y ^{2}}

= \frac{x}{8 + x ^{2} - 2 y ^{2}}

\int \frac{t ^{2} cos ( 2 t ^{3} )}{csc ( 10 t ^{3} )} d t

x \to \infty lim (x^{2} - 1)

\int x (x + 1) d x

\frac{\partial}{\partial y} (ln (x))

n = 1 \sum \infty 4^{n}

What is (\partial)/(\partial x)(sqrt(8+x^2-2y^2)) ?
The answer to (\partial)/(\partial x)(sqrt(8+x^2-2y^2)) is x/(sqrt(8+x^2-2y^2))