What is (\partial)/(\partial x)((x^2+y^2)^{0.5}) ?

The answer to (\partial)/(\partial x)((x^2+y^2)^{0.5}) is x/((x^2+y^2)^{1/2)}

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(\partial)/(\partial x)((x^2+y^2)^{0.5})

\frac{\partial}{\partial x} ((x^{2} + y^{2})^{0.5})

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

Solution steps

\frac{\partial}{\partial x} ((x^{2} + y^{2})^{0.5})

Treat

y

as a constant

Apply the chain rule:

\frac{0.5}{( x ^{2} + y ^{2} ) ^{0.5}} \frac{\partial}{\partial x} (x^{2} + y^{2})

= \frac{0.5}{( x ^{2} + y ^{2} ) ^{0.5}} \frac{\partial}{\partial x} (x^{2} + y^{2})

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

= \frac{0.5}{( x ^{2} + y ^{2} ) ^{0.5}} \cdot 2 x

Simplify

\frac{0.5}{( x ^{2} + y ^{2} ) ^{\frac{1}{2}}} \cdot 2 x : \frac{x}{( x ^{2} + y ^{2} ) ^{\frac{1}{2}}}

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

y^{^{''}} = 1

f (2) = x^{3} - 2 x

x \to 2 - lim (x + 7)

\frac{\partial}{\partial x} (20 - (3 x^{2} + y^{2}))

\frac{d}{d x} (\frac{5 x}{2})

What is (\partial)/(\partial x)((x^2+y^2)^{0.5}) ?
The answer to (\partial)/(\partial x)((x^2+y^2)^{0.5}) is x/((x^2+y^2)^{1/2)}