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

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

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

- \frac{- x + m}{( m - x ) ^{2} + y ^{2}}

Solution steps

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

Treat

m, y

as constants

Apply the chain rule:

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

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

\frac{\partial}{\partial x} ((m - x)^{2} + y^{2}) = - 2 (- x + m)

= \frac{1}{2 ( m - x ) ^{2} + y ^{2}} (- 2 (- x + m))

Simplify

\frac{1}{2 ( m - x ) ^{2} + y ^{2}} (- 2 (- x + m)) : - \frac{- x + m}{( m - x ) ^{2} + y ^{2}}

= - \frac{- x + m}{( m - x ) ^{2} + y ^{2}}

x \to 3 lim (\frac{4 x + 8}{x - 5})

y = e^{x}, at x = 0

\frac{d}{d x} (\frac{200}{1 + e ^{5 - x}})

\int \frac{12 x}{( x - 1 ) ( x ^{2} + 2 x + 3 )} d x

(1.2) (3.3)

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