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

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

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

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

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Popular >

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

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

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

\int_{0}^{1} (e^{x} + 1)^{2} d x

\int 3 - x x^{2} d x

\int \frac{( x ^{3} - 2 x )}{x} d x

\frac{9}{( s ^{2} + 4 s + 9 )}

y = 8 x^{4}, at x = 2

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