What is (\partial)/(\partial x)(sqrt(96-5x^2-3y^2)) ?

The answer to (\partial)/(\partial x)(sqrt(96-5x^2-3y^2)) is -(5x)/(sqrt(96-5x^2-3y^2))

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(\partial)/(\partial x)(sqrt(96-5x^2-3y^2))

\frac{\partial}{\partial x} (96 - 5 x^{2} - 3 y^{2})

- \frac{5 x}{96 - 5 x ^{2} - 3 y ^{2}}

Solution steps

\frac{\partial}{\partial x} (96 - 5 x^{2} - 3 y^{2})

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 96 - 5 x ^{2} - 3 y ^{2}} \frac{\partial}{\partial x} (96 - 5 x^{2} - 3 y^{2})

= \frac{1}{2 96 - 5 x ^{2} - 3 y ^{2}} \frac{\partial}{\partial x} (96 - 5 x^{2} - 3 y^{2})

\frac{\partial}{\partial x} (96 - 5 x^{2} - 3 y^{2}) = - 10 x

= \frac{1}{2 96 - 5 x ^{2} - 3 y ^{2}} (- 10 x)

Simplify

\frac{1}{2 96 - 5 x ^{2} - 3 y ^{2}} (- 10 x) : - \frac{5 x}{96 - 5 x ^{2} - 3 y ^{2}}

= - \frac{5 x}{96 - 5 x ^{2} - 3 y ^{2}}

f (x) = x^{3} + 1

\int \frac{e ^{x}}{e ^{3 x} + e ^{2 x}} d x

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

\int \frac{1}{4 x + 1} d x

\frac{\partial}{\partial x} (\frac{7}{x})

What is (\partial)/(\partial x)(sqrt(96-5x^2-3y^2)) ?
The answer to (\partial)/(\partial x)(sqrt(96-5x^2-3y^2)) is -(5x)/(sqrt(96-5x^2-3y^2))