What is (\partial)/(\partial x)(sqrt(90-4x^2-1y^2)) ?

The answer to (\partial)/(\partial x)(sqrt(90-4x^2-1y^2)) is -(4x)/(sqrt(90-4x^2-y^2))

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(\partial)/(\partial x)(sqrt(90-4x^2-1y^2))

\frac{\partial}{\partial x} (90 - 4 x^{2} - 1 y^{2})

- \frac{4 x}{90 - 4 x ^{2} - y ^{2}}

Solution steps

\frac{\partial}{\partial x} (90 - 4 x^{2} - 1 \cdot y^{2})

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 90 - 4 x ^{2} - 1 \cdot y ^{2}} \frac{\partial}{\partial x} (90 - 4 x^{2} - 1 \cdot y^{2})

= \frac{1}{2 90 - 4 x ^{2} - 1 \cdot y ^{2}} \frac{\partial}{\partial x} (90 - 4 x^{2} - 1 \cdot y^{2})

\frac{\partial}{\partial x} (90 - 4 x^{2} - 1 \cdot y^{2}) = - 8 x

= \frac{1}{2 90 - 4 x ^{2} - 1 \cdot y ^{2}} (- 8 x)

Simplify

\frac{1}{2 90 - 4 x ^{2} - 1 \cdot y ^{2}} (- 8 x) : - \frac{4 x}{90 - 4 x ^{2} - y ^{2}}

= - \frac{4 x}{90 - 4 x ^{2} - y ^{2}}

y^{^{'}} = \frac{t ^{2}}{y} (1 + t^{3})

\int_{0}^{13} 8 x d x

(3 x + y e^{\frac{y}{x}}) d x - x e^{\frac{y}{x}} d y = 0

- 10 x^{2} y + y^{^{'}} = 5 x^{2}

x \to 5 + lim (lo g_{3} (x - 5))

What is (\partial)/(\partial x)(sqrt(90-4x^2-1y^2)) ?
The answer to (\partial)/(\partial x)(sqrt(90-4x^2-1y^2)) is -(4x)/(sqrt(90-4x^2-y^2))