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

The d/(d{x)}(({x}^2+{y}^2+{z}^2)^{3/2}) is 3{x}({x}^2+{y}^2+{z}^2)^{1/2}

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

The first d/(d{x)}(({x}^2+{y}^2+{z}^2)^{3/2}) is 3{x}({x}^2+{y}^2+{z}^2)^{1/2}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Apply the chain rule:

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

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

Simplify

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

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

x^{4} + 4

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

y^{^{''}} - 9 y = 54

(- 8, - 6), (- 18, 6)

y = x^{2} - 3 x - 3, (2, - 5)

What is the d/(d{x)}(({x}^2+{y}^2+{z}^2)^{3/2}) ?
The d/(d{x)}(({x}^2+{y}^2+{z}^2)^{3/2}) is 3{x}({x}^2+{y}^2+{z}^2)^{1/2}
What is the first d/(d{x)}(({x}^2+{y}^2+{z}^2)^{3/2}) ?
The first d/(d{x)}(({x}^2+{y}^2+{z}^2)^{3/2}) is 3{x}({x}^2+{y}^2+{z}^2)^{1/2}