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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (3 - 3 x^{2} + y^{2}) = - 6 x

= \frac{1}{2 3 - 3 x ^{2} + y ^{2}} (- 6 x)

Simplify

\frac{1}{2 3 - 3 x ^{2} + y ^{2}} (- 6 x) : - \frac{3 x}{3 - 3 x ^{2} + y ^{2}}

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

(8 + x) y^{^{'}} = 5 y

\frac{10}{( s ( s ^{2} + 2 s + 20 ) )}

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

\int (1 + tan (x))^{5} sec^{2} (x) d x

y = 3 cos (2 x)

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