What is (\partial)/(\partial x)(ln(x^6y)) ?

The answer to (\partial)/(\partial x)(ln(x^6y)) is 6/x

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^6y))

\frac{\partial}{\partial x} (ln (x^{6} y))

\frac{6}{x}

Solution steps

\frac{\partial}{\partial x} (ln (x^{6} y))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{x ^{6} y} \frac{\partial}{\partial x} (x^{6} y)

= \frac{1}{x ^{6} y} \frac{\partial}{\partial x} (x^{6} y)

\frac{\partial}{\partial x} (x^{6} y) = 6 y x^{5}

= \frac{1}{x ^{6} y} \cdot 6 y x^{5}

Simplify

\frac{1}{x ^{6} y} \cdot 6 y x^{5} : \frac{6}{x}

= \frac{6}{x}

\frac{d y}{d x} + \frac{y}{x} = 8 x^{5} y^{2}

\int_{0}^{6} \frac{8 t}{( t - 7 ) ^{2}} d t

\frac{\partial}{\partial x} (\frac{z ( x + y )}{x + y + z})

x^{^{'}} = - 2 x

x \to - 10 lim (- (\frac{1}{x + 10}))

What is (\partial)/(\partial x)(ln(x^6y)) ?
The answer to (\partial)/(\partial x)(ln(x^6y)) is 6/x