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

The d/(d{x)}(({z})/(({x)^2+{y}^2+{z}^2)^{3/2}}) is -(3{z)/x}{({x}^2+{y}^2+{z}^2)^{5/2}}

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

The first d/(d{x)}(({z})/(({x)^2+{y}^2+{z}^2)^{3/2}}) is -(3{z)/x}{({x}^2+{y}^2+{z}^2)^{5/2}}

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

- \frac{3 z x}{( x ^{2} + y ^{2} + z ^{2} ) ^{\frac{5}{2}}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{3}{2 ( x ^{2} + y ^{2} + z ^{2} ) ^{\frac{5}{2}}} \frac{d}{d x} (x^{2} + y^{2} + z^{2})

= - \frac{3}{2 ( x ^{2} + y ^{2} + z ^{2} ) ^{\frac{5}{2}}} \frac{d}{d x} (x^{2} + y^{2} + z^{2})

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

= z (- \frac{3}{2 ( x ^{2} + y ^{2} + z ^{2} ) ^{\frac{5}{2}}} \cdot 2 x)

Simplify

z (- \frac{3}{2 ( x ^{2} + y ^{2} + z ^{2} ) ^{\frac{5}{2}}} \cdot 2 x) : - \frac{3 z x}{( x ^{2} + y ^{2} + z ^{2} ) ^{\frac{5}{2}}}

= - \frac{3 z x}{( x ^{2} + y ^{2} + z ^{2} ) ^{\frac{5}{2}}}

\frac{1}{( s + 1 ) ( s + 2 ) ^{2}}

\frac{1}{3 - 2 x}

\int \frac{1}{( x ^{2} - 4 ) ^{\frac{1}{2}}} d x

(1 + e^{x}) y y^{^{'}} = e^{x}, y (0) = 1

f (x) = 3 x^{2} - 8 x - x

What is the d/(d{x)}(({z})/(({x)^2+{y}^2+{z}^2)^{3/2}}) ?
The d/(d{x)}(({z})/(({x)^2+{y}^2+{z}^2)^{3/2}}) is -(3{z)/x}{({x}^2+{y}^2+{z}^2)^{5/2}}
What is the first d/(d{x)}(({z})/(({x)^2+{y}^2+{z}^2)^{3/2}}) ?
The first d/(d{x)}(({z})/(({x)^2+{y}^2+{z}^2)^{3/2}}) is -(3{z)/x}{({x}^2+{y}^2+{z}^2)^{5/2}}