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

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

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

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

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Popular >

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int e^{- x} cos (9 x) d x

\frac{d}{d x} (x (5 x + 9)^{\frac{1}{3}})

\int_{0}^{1} 6 cos (\frac{π t}{2}) d t

\frac{d}{d x} ((4 - x)^{2})

\int \frac{7}{x ^{2} + 7} d x

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