What is (\partial)/(\partial x)(sqrt(20-x^2-7y^2)) ?

The answer to (\partial)/(\partial x)(sqrt(20-x^2-7y^2)) is -x/(sqrt(20-x^2-7y^2))

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(\partial)/(\partial x)(sqrt(20-x^2-7y^2))

\frac{\partial}{\partial x} (20 - x^{2} - 7 y^{2})

- \frac{x}{20 - x ^{2} - 7 y ^{2}}

Solution steps

\frac{\partial}{\partial x} (20 - x^{2} - 7 y^{2})

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 20 - x ^{2} - 7 y ^{2}} \frac{\partial}{\partial x} (20 - x^{2} - 7 y^{2})

= \frac{1}{2 20 - x ^{2} - 7 y ^{2}} \frac{\partial}{\partial x} (20 - x^{2} - 7 y^{2})

\frac{\partial}{\partial x} (20 - x^{2} - 7 y^{2}) = - 2 x

= \frac{1}{2 20 - x ^{2} - 7 y ^{2}} (- 2 x)

Simplify

\frac{1}{2 20 - x ^{2} - 7 y ^{2}} (- 2 x) : - \frac{x}{20 - x ^{2} - 7 y ^{2}}

= - \frac{x}{20 - x ^{2} - 7 y ^{2}}

\frac{d}{d x} (ln (\frac{1 + e ^{x}}{1 - e ^{x}}))

\int (x - 1)^{3} d x

\int \frac{1}{( x + 1 ) ^{3}} d x

x \to 2 lim (4 - x^{2})

x \to 2 lim (5 x^{4})

What is (\partial)/(\partial x)(sqrt(20-x^2-7y^2)) ?
The answer to (\partial)/(\partial x)(sqrt(20-x^2-7y^2)) is -x/(sqrt(20-x^2-7y^2))