What is (\partial)/(\partial y)(sqrt(4-x^2-3y^2)) ?

The answer to (\partial)/(\partial y)(sqrt(4-x^2-3y^2)) is -(3y)/(sqrt(4-x^2-3y^2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial y)(sqrt(4-x^2-3y^2))

\frac{\partial}{\partial y} (4 - x^{2} - 3 y^{2})

- \frac{3 y}{4 - x ^{2} - 3 y ^{2}}

Solution steps

\frac{\partial}{\partial y} (4 - x^{2} - 3 y^{2})

Treat

x

as a constant

Apply the chain rule:

\frac{1}{2 4 - x ^{2} - 3 y ^{2}} \frac{\partial}{\partial y} (4 - x^{2} - 3 y^{2})

= \frac{1}{2 4 - x ^{2} - 3 y ^{2}} \frac{\partial}{\partial y} (4 - x^{2} - 3 y^{2})

\frac{\partial}{\partial y} (4 - x^{2} - 3 y^{2}) = - 6 y

= \frac{1}{2 4 - x ^{2} - 3 y ^{2}} (- 6 y)

Simplify

\frac{1}{2 4 - x ^{2} - 3 y ^{2}} (- 6 y) : - \frac{3 y}{4 - x ^{2} - 3 y ^{2}}

= - \frac{3 y}{4 - x ^{2} - 3 y ^{2}}

\int \frac{1}{7 - x} d x

\int \frac{x ^{2} + 1}{( x - 2 ) ^{2}} d x

x \to \frac{π}{6} lim (cot (x))

f (x) = x - 7 3 x

\int (12 x) d x

What is (\partial)/(\partial y)(sqrt(4-x^2-3y^2)) ?
The answer to (\partial)/(\partial y)(sqrt(4-x^2-3y^2)) is -(3y)/(sqrt(4-x^2-3y^2))