What is (\partial)/(\partial x)(sqrt(21-3x^2-4y^2)) ?

The answer to (\partial)/(\partial x)(sqrt(21-3x^2-4y^2)) is -(3x)/(sqrt(21-3x^2-4y^2))

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(\partial)/(\partial x)(sqrt(21-3x^2-4y^2))

\frac{\partial}{\partial x} (21 - 3 x^{2} - 4 y^{2})

- \frac{3 x}{21 - 3 x ^{2} - 4 y ^{2}}

Solution steps

\frac{\partial}{\partial x} (21 - 3 x^{2} - 4 y^{2})

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 21 - 3 x ^{2} - 4 y ^{2}} \frac{\partial}{\partial x} (21 - 3 x^{2} - 4 y^{2})

= \frac{1}{2 21 - 3 x ^{2} - 4 y ^{2}} \frac{\partial}{\partial x} (21 - 3 x^{2} - 4 y^{2})

\frac{\partial}{\partial x} (21 - 3 x^{2} - 4 y^{2}) = - 6 x

= \frac{1}{2 21 - 3 x ^{2} - 4 y ^{2}} (- 6 x)

Simplify

\frac{1}{2 21 - 3 x ^{2} - 4 y ^{2}} (- 6 x) : - \frac{3 x}{21 - 3 x ^{2} - 4 y ^{2}}

= - \frac{3 x}{21 - 3 x ^{2} - 4 y ^{2}}

\frac{d}{d x} (7^{- 4 x + 1 + 2 x^{- 1}})

\frac{d}{d x} (x (- \frac{1}{10} x + 610))

x \to 1 lim (2^{0})

\int_{2}^{3} 1 d x

\frac{x ^{2} - 9}{x - 3}

What is (\partial)/(\partial x)(sqrt(21-3x^2-4y^2)) ?
The answer to (\partial)/(\partial x)(sqrt(21-3x^2-4y^2)) is -(3x)/(sqrt(21-3x^2-4y^2))