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

The derivative of ln(x^2+y^2+1) is (2x+2y\frac{dy)/(dx)}{x^2+y^2+1}

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

The first derivative of ln(x^2+y^2+1) is (2x+2y\frac{dy)/(dx)}{x^2+y^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} + y^{2} + 1))

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to \infty + lim (\frac{( 5 x ^{3} + 7 x ^{2} - 8 x + 9 )}{11 x ^{2} + 7 x - 6})

\int sin^{4} (7 x) d x

\frac{1}{( s - 5 ) ^{2}}

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

y^{^{''}} + 4 y^{^{'}} + 13 y = 0

What is the derivative of ln(x^2+y^2+1) ?
The derivative of ln(x^2+y^2+1) is (2x+2y\frac{dy)/(dx)}{x^2+y^2+1}
What is the first derivative of ln(x^2+y^2+1) ?
The first derivative of ln(x^2+y^2+1) is (2x+2y\frac{dy)/(dx)}{x^2+y^2+1}