What is (\partial)/(\partial x)(ln(1+x^2)) ?

The answer to (\partial)/(\partial x)(ln(1+x^2)) is (2x)/(1+x^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(ln(1+x^2))

\frac{\partial}{\partial x} (ln (1 + x^{2}))

\frac{2 x}{1 + x ^{2}}

Solution steps

\frac{\partial}{\partial x} (ln (1 + x^{2}))

Apply the chain rule:

\frac{1}{1 + x ^{2}} \frac{\partial}{\partial x} (1 + x^{2})

= \frac{1}{1 + x ^{2}} \frac{\partial}{\partial x} (1 + x^{2})

\frac{\partial}{\partial x} (1 + x^{2}) = 2 x

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

Simplify

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

= \frac{2 x}{1 + x ^{2}}

y = 4 x^{2} - 3 x + 3, (1, 4)

\int x^{3} - 3 d x

\frac{d}{d θ} (e^{t a n (θ)})

\int_{0}^{1} \frac{y}{e ^{5 y}} d y

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

What is (\partial)/(\partial x)(ln(1+x^2)) ?
The answer to (\partial)/(\partial x)(ln(1+x^2)) is (2x)/(1+x^2)