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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (2 - 2 x^{2} + y^{2}) = - 4 x

= \frac{1}{2 2 - 2 x ^{2} + y ^{2}} (- 4 x)

Simplify

\frac{1}{2 2 - 2 x ^{2} + y ^{2}} (- 4 x) : - \frac{2 x}{2 - 2 x ^{2} + y ^{2}}

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

(5.2) (6.4)

x \to - 9 + lim (8 x + 72)

f (x) = sin^{4} (x)

4 + x

\int \frac{1}{( x ^{2} - x - 2 ) ( x - 2 )} d x

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