en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of ln(2xy+4)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

\frac{1}{2 x y + 4} \frac{d}{d x} (2 x y + 4)

= \frac{1}{2 x y + 4} \frac{d}{d x} (2 x y + 4)

\frac{d}{d x} (2 x y + 4) = 2 (x \frac{d y}{d x} + y)

= \frac{1}{2 x y + 4} \cdot 2 (x \frac{d y}{d x} + y)

Simplify

\frac{1}{2 x y + 4} \cdot 2 (x \frac{d y}{d x} + y) : \frac{x \frac{d y}{d x} + y}{x y + 2}

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

Popular Examples

integral of e^{1/2 x}

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

integral of sec(t)(8sec(t)+7tan(t))

\int sec (t) (8 sec (t) + 7 tan (t)) d t

derivative of f(x)=2x^2+x-1,\at a=-1 derivative of

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

y^'=5y^2+xy^2,y(0)=1

y^{^{'}} = 5 y^{2} + x y^{2}, y (0) = 1

derivative of (-8x-2/(9x-4))

\frac{d}{d x} (\frac{- 8 x - 2}{9 x - 4})

Frequently Asked Questions (FAQ)

What is the derivative of ln(2xy+4) ?
The derivative of ln(2xy+4) is (x\frac{dy)/(dx)+y}{xy+2}
What is the first derivative of ln(2xy+4) ?
The first derivative of ln(2xy+4) is (x\frac{dy)/(dx)+y}{xy+2}