What is (\partial)/(\partial y)(3x(y-1)^{1/3}) ?

The answer to (\partial)/(\partial y)(3x(y-1)^{1/3}) is x/((y-1)^{2/3)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial y)(3x(y-1)^{1/3})

\frac{\partial}{\partial y} (3 x (y - 1)^{\frac{1}{3}})

\frac{x}{( y - 1 ) ^{\frac{2}{3}}}

Solution steps

\frac{\partial}{\partial y} (3 x (y - 1)^{\frac{1}{3}})

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 x \frac{\partial}{\partial y} ((y - 1)^{\frac{1}{3}})

Apply the chain rule:

\frac{1}{3 ( y - 1 ) ^{\frac{2}{3}}} \frac{\partial}{\partial y} (y - 1)

= \frac{1}{3 ( y - 1 ) ^{\frac{2}{3}}} \frac{\partial}{\partial y} (y - 1)

\frac{\partial}{\partial y} (y - 1) = 1

= 3 x \frac{1}{3 ( y - 1 ) ^{\frac{2}{3}}} \cdot 1

Simplify

3 x \frac{1}{3 ( y - 1 ) ^{\frac{2}{3}}} \cdot 1 : \frac{x}{( y - 1 ) ^{\frac{2}{3}}}

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

\frac{d}{d x} (- \frac{9 x}{y})

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

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

(1.85) (5.1)

\int x 4^{x^{2} + 5} d x

What is (\partial)/(\partial y)(3x(y-1)^{1/3}) ?
The answer to (\partial)/(\partial y)(3x(y-1)^{1/3}) is x/((y-1)^{2/3)}