What is (\partial)/(\partial x)(sqrt(17-4x^2-y^2)) ?

The answer to (\partial)/(\partial x)(sqrt(17-4x^2-y^2)) is -(4x)/(sqrt(17-4x^2-y^2))

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(\partial)/(\partial x)(sqrt(17-4x^2-y^2))

\frac{\partial}{\partial x} (17 - 4 x^{2} - y^{2})

- \frac{4 x}{17 - 4 x ^{2} - y ^{2}}

Solution steps

\frac{\partial}{\partial x} (17 - 4 x^{2} - y^{2})

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 17 - 4 x ^{2} - y ^{2}} \frac{\partial}{\partial x} (17 - 4 x^{2} - y^{2})

= \frac{1}{2 17 - 4 x ^{2} - y ^{2}} \frac{\partial}{\partial x} (17 - 4 x^{2} - y^{2})

\frac{\partial}{\partial x} (17 - 4 x^{2} - y^{2}) = - 8 x

= \frac{1}{2 17 - 4 x ^{2} - y ^{2}} (- 8 x)

Simplify

\frac{1}{2 17 - 4 x ^{2} - y ^{2}} (- 8 x) : - \frac{4 x}{17 - 4 x ^{2} - y ^{2}}

= - \frac{4 x}{17 - 4 x ^{2} - y ^{2}}

\frac{\partial}{\partial x} (\frac{y}{cos ( x )})

\frac{d}{d x} (\frac{4}{5} ln ((9 x^{2} - 6)^{7}))

\int_{2}^{4} \frac{( 2 x - 3 )}{6} d x

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

x \to \infty lim (\frac{7 ^{12} - 2176782336}{7 ^{11}})

What is (\partial)/(\partial x)(sqrt(17-4x^2-y^2)) ?
The answer to (\partial)/(\partial x)(sqrt(17-4x^2-y^2)) is -(4x)/(sqrt(17-4x^2-y^2))