What is (\partial)/(\partial x)(ln(x+2y+6z)) ?

The answer to (\partial)/(\partial x)(ln(x+2y+6z)) is 1/(x+2y+6z)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(ln(x+2y+6z))

\frac{\partial}{\partial x} (ln (x + 2 y + 6 z))

\frac{1}{x + 2 y + 6 z}

Solution steps

\frac{\partial}{\partial x} (ln (x + 2 y + 6 z))

Treat

y, z

as constants

Apply the chain rule:

\frac{1}{x + 2 y + 6 z} \frac{\partial}{\partial x} (x + 2 y + 6 z)

= \frac{1}{x + 2 y + 6 z} \frac{\partial}{\partial x} (x + 2 y + 6 z)

\frac{\partial}{\partial x} (x + 2 y + 6 z) = 1

= \frac{1}{x + 2 y + 6 z} \cdot 1

Simplify

= \frac{1}{x + 2 y + 6 z}

\frac{d}{d x} (A e^{- \frac{3}{2} x} + B e^{3 x} + C x e^{3 x} + d x^{2} e^{3 x})

\frac{d}{d x} ((x^{2} + 4 x - 5)^{4})

\int x^{2} cos (\frac{x}{2}) d x

e^{t}

\int \frac{t ^{2}}{1 - t ^{6}} d t

What is (\partial)/(\partial x)(ln(x+2y+6z)) ?
The answer to (\partial)/(\partial x)(ln(x+2y+6z)) is 1/(x+2y+6z)