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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Apply exponent rule:

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

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

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

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

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

Simplify

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

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

x \to 1 lim (\frac{x ^{2} - 3 x + 2}{x ^{3} - 1})

\int \frac{3}{x ^{2} 25 - x ^{2}} d x

f (x) = \frac{2}{x + 2}

\frac{\partial}{\partial y} ((x^{2} + y) e^{\frac{y}{2}})

\int e^{- 2 x} sin (2 x) d x

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