What is the d/(d{y)}(({x}^2+{y}^2+{z}^2)^{-1/2}) ?

The d/(d{y)}(({x}^2+{y}^2+{z}^2)^{-1/2}) is -({y})/(({x)^2+{y}^2+{z}^2)^{3/2}}

What is the first d/(d{y)}(({x}^2+{y}^2+{z}^2)^{-1/2}) ?

The first d/(d{y)}(({x}^2+{y}^2+{z}^2)^{-1/2}) is -({y})/(({x)^2+{y}^2+{z}^2)^{3/2}}

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int 54 - 18 z - 6 z^{2} + 2 z^{3} d z

\int_{0}^{1} 2 x 5^{x} d x

v^{\frac{3}{2}} (v + c e^{x})

(y + x cos^{2} (\frac{y}{x})) d x - x d y = 0

\int \frac{6 x}{1 + x ^{4}} d x

What is the d/(d{y)}(({x}^2+{y}^2+{z}^2)^{-1/2}) ?
The d/(d{y)}(({x}^2+{y}^2+{z}^2)^{-1/2}) is -({y})/(({x)^2+{y}^2+{z}^2)^{3/2}}
What is the first d/(d{y)}(({x}^2+{y}^2+{z}^2)^{-1/2}) ?
The first d/(d{y)}(({x}^2+{y}^2+{z}^2)^{-1/2}) is -({y})/(({x)^2+{y}^2+{z}^2)^{3/2}}