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))

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(\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}}

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))