en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of ln(x^2+3x+3)

Solution

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

Solution

\frac{2 x + 3}{x ^{2} + 3 x + 3}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{2 x + 3}{x ^{2} + 3 x + 3}

Popular Examples

derivative of f(x)=4x^4+3x^2-1 derivative of

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

\frac{d y}{d x} = 4 y x

integral of cos^7(x)

\int cos^{7} (x) d x

(\partial)/(\partial x)(ln(4+x^2y^2))

\frac{\partial}{\partial x} (ln (4 + x^{2} y^{2}))

tangent of (x^2+y^2)^2=4x^2y,(1,1)tangent of

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

Frequently Asked Questions (FAQ)

What is the derivative of ln(x^2+3x+3) ?
The derivative of ln(x^2+3x+3) is (2x+3)/(x^2+3x+3)
What is the first derivative of ln(x^2+3x+3) ?
The first derivative of ln(x^2+3x+3) is (2x+3)/(x^2+3x+3)