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

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

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

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

\frac{x}{x ^{2} + y ^{2} + z ^{2}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{x}{x ^{2} + y ^{2} + z ^{2}}

\frac{\partial}{\partial x} (x^{5} + y^{5})

\frac{\partial}{\partial x} ((x y)^{0.5})

y^{^{'}} + sin (t) y = - sin (t), y (0) = 3

80 t^{2}

f (x) = x^{2} (1 - x)^{2}, at x = 2

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