What is (\partial)/(\partial x)(sqrt(61-x^2-3y^2)) ?

The answer to (\partial)/(\partial x)(sqrt(61-x^2-3y^2)) is -x/(sqrt(61-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 x)(sqrt(61-x^2-3y^2))

\frac{\partial}{\partial x} (61 - x^{2} - 3 y^{2})

- \frac{x}{61 - x ^{2} - 3 y ^{2}}

Solution steps

\frac{\partial}{\partial x} (61 - x^{2} - 3 y^{2})

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 61 - x ^{2} - 3 y ^{2}} \frac{\partial}{\partial x} (61 - x^{2} - 3 y^{2})

= \frac{1}{2 61 - x ^{2} - 3 y ^{2}} \frac{\partial}{\partial x} (61 - x^{2} - 3 y^{2})

\frac{\partial}{\partial x} (61 - x^{2} - 3 y^{2}) = - 2 x

= \frac{1}{2 61 - x ^{2} - 3 y ^{2}} (- 2 x)

Simplify

\frac{1}{2 61 - x ^{2} - 3 y ^{2}} (- 2 x) : - \frac{x}{61 - x ^{2} - 3 y ^{2}}

= - \frac{x}{61 - x ^{2} - 3 y ^{2}}

\int_{2}^{5} x^{2} d x

x \to 0 + lim (7 sin (x) ln (x))

\int sin (11 x) ln (sin (11 x)) d x

f (x) = x^{3} - 2 x + 1, at x = 0

\frac{8}{( 1 - x ) ^{2}}

What is (\partial)/(\partial x)(sqrt(61-x^2-3y^2)) ?
The answer to (\partial)/(\partial x)(sqrt(61-x^2-3y^2)) is -x/(sqrt(61-x^2-3y^2))