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

The d/(d{y)}(({x})/(({x)^2+{y}^2+{z}^2)^2}) is -(4{x)/y}{({x}^2+{y}^2+{z}^2)^3}

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

The first d/(d{y)}(({x})/(({x)^2+{y}^2+{z}^2)^2}) is -(4{x)/y}{({x}^2+{y}^2+{z}^2)^3}

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Popular >

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

- \frac{4 x y}{( x ^{2} + y ^{2} + z ^{2} ) ^{3}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

x (- \frac{2}{( x ^{2} + y ^{2} + z ^{2} ) ^{3}} \cdot 2 y) : - \frac{4 x y}{( x ^{2} + y ^{2} + z ^{2} ) ^{3}}

= - \frac{4 x y}{( x ^{2} + y ^{2} + z ^{2} ) ^{3}}

\int - 3 csc (x) cot (x) d x

f (x) (6 x^{2} - 3) (1. 5^{x})

\frac{\partial}{\partial x} (y^{6} sin (3 x))

\int \frac{5}{9 - x ^{2}} d x

\frac{d}{d x} (sin (x) + x^{2} e^{y} + 5)

What is the d/(d{y)}(({x})/(({x)^2+{y}^2+{z}^2)^2}) ?
The d/(d{y)}(({x})/(({x)^2+{y}^2+{z}^2)^2}) is -(4{x)/y}{({x}^2+{y}^2+{z}^2)^3}
What is the first d/(d{y)}(({x})/(({x)^2+{y}^2+{z}^2)^2}) ?
The first d/(d{y)}(({x})/(({x)^2+{y}^2+{z}^2)^2}) is -(4{x)/y}{({x}^2+{y}^2+{z}^2)^3}