What is (\partial)/(\partial x)((x^2+y^2)^{-1/2}) ?

The answer to (\partial)/(\partial x)((x^2+y^2)^{-1/2}) is -x/((x^2+y^2)^{3/2)}

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

1 + e^{0.5499 - 0.09 x}

y = cos (ln (4 x^{3}))

y = e^{x} sin (x) + cos (x) e^{x}

f (x) = ((6 x^{2} - 6 x + 6)^{5})

3 x^{3} ln (x^{2})

What is (\partial)/(\partial x)((x^2+y^2)^{-1/2}) ?
The answer to (\partial)/(\partial x)((x^2+y^2)^{-1/2}) is -x/((x^2+y^2)^{3/2)}