What is the derivative of ln(x^2+sqrt(x^2+1)) ?

The derivative of ln(x^2+sqrt(x^2+1)) is (2xsqrt(x^2+1)+x)/((x^2+sqrt(x^2+1))\sqrt{x^2+1)}

What is the first derivative of ln(x^2+sqrt(x^2+1)) ?

The first derivative of ln(x^2+sqrt(x^2+1)) is (2xsqrt(x^2+1)+x)/((x^2+sqrt(x^2+1))\sqrt{x^2+1)}

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} + x^{2} + 1))

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int \frac{1}{1 - 2 x ^{2}} d x

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

\int_{0}^{9} x d x

f (x) = x^{4} + 2 x^{2}, at x = 1

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

What is the derivative of ln(x^2+sqrt(x^2+1)) ?
The derivative of ln(x^2+sqrt(x^2+1)) is (2xsqrt(x^2+1)+x)/((x^2+sqrt(x^2+1))\sqrt{x^2+1)}
What is the first derivative of ln(x^2+sqrt(x^2+1)) ?
The first derivative of ln(x^2+sqrt(x^2+1)) is (2xsqrt(x^2+1)+x)/((x^2+sqrt(x^2+1))\sqrt{x^2+1)}