What is (\partial)/(\partial x)(sqrt(15-2x^2-y^2)) ?

The answer to (\partial)/(\partial x)(sqrt(15-2x^2-y^2)) is -(2x)/(sqrt(15-2x^2-y^2))

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(\partial)/(\partial x)(sqrt(15-2x^2-y^2))

\frac{\partial}{\partial x} (15 - 2 x^{2} - y^{2})

- \frac{2 x}{15 - 2 x ^{2} - y ^{2}}

Solution steps

\frac{\partial}{\partial x} (15 - 2 x^{2} - y^{2})

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 15 - 2 x ^{2} - y ^{2}} \frac{\partial}{\partial x} (15 - 2 x^{2} - y^{2})

= \frac{1}{2 15 - 2 x ^{2} - y ^{2}} \frac{\partial}{\partial x} (15 - 2 x^{2} - y^{2})

\frac{\partial}{\partial x} (15 - 2 x^{2} - y^{2}) = - 4 x

= \frac{1}{2 15 - 2 x ^{2} - y ^{2}} (- 4 x)

Simplify

\frac{1}{2 15 - 2 x ^{2} - y ^{2}} (- 4 x) : - \frac{2 x}{15 - 2 x ^{2} - y ^{2}}

= - \frac{2 x}{15 - 2 x ^{2} - y ^{2}}

(3 + x^{4})^{\frac{4}{5}}

x \to 0 + lim (\frac{10}{x ^{2}})

f (x) = 17 e^{x} - e x^{e}

f (x) = \frac{x}{x + 2}

\frac{d y}{d t} = 9 t^{2}

What is (\partial)/(\partial x)(sqrt(15-2x^2-y^2)) ?
The answer to (\partial)/(\partial x)(sqrt(15-2x^2-y^2)) is -(2x)/(sqrt(15-2x^2-y^2))