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

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

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(\partial)/(\partial x)(sqrt(x^2+y^2)-x)

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

\frac{x}{x ^{2} + y ^{2}} - 1

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{\partial}{\partial x} (x) = 1

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

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

y = x^{2} sin (π x)

\frac{\partial}{\partial x} (- 5 x^{2} - 2 x y - 3 y^{2})

arccot (\frac{x}{9})

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

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