What is (\partial)/(\partial x)((2(y^2-4))/(3(x-1)^{1/3)}) ?

The answer to (\partial)/(\partial x)((2(y^2-4))/(3(x-1)^{1/3)}) is -(2(y^2-4))/(9(x-1)^{4/3)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)((2(y^2-4))/(3(x-1)^{1/3)})

\frac{\partial}{\partial x} (\frac{2 ( y ^{2} - 4 )}{3 ( x - 1 ) ^{\frac{1}{3}}})

- \frac{2 ( y ^{2} - 4 )}{9 ( x - 1 ) ^{\frac{4}{3}}}

Solution steps

\frac{\partial}{\partial x} (\frac{2 ( y ^{2} - 4 )}{3 ( x - 1 ) ^{\frac{1}{3}}})

Treat

y

as a constant

Take the constant out:

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

= \frac{2 ( y ^{2} - 4 )}{3} \frac{\partial}{\partial x} (\frac{1}{( x - 1 ) ^{\frac{1}{3}}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= \frac{2 ( y ^{2} - 4 )}{3} \frac{\partial}{\partial x} ((x - 1)^{- \frac{1}{3}})

Apply the chain rule:

- \frac{1}{3 ( x - 1 ) ^{\frac{4}{3}}} \frac{\partial}{\partial x} (x - 1)

= - \frac{1}{3 ( x - 1 ) ^{\frac{4}{3}}} \frac{\partial}{\partial x} (x - 1)

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

= \frac{2 ( y ^{2} - 4 )}{3} (- \frac{1}{3 ( x - 1 ) ^{\frac{4}{3}}} \cdot 1)

Simplify

\frac{2 ( y ^{2} - 4 )}{3} (- \frac{1}{3 ( x - 1 ) ^{\frac{4}{3}}} \cdot 1) : - \frac{2 ( y ^{2} - 4 )}{9 ( x - 1 ) ^{\frac{4}{3}}}

= - \frac{2 ( y ^{2} - 4 )}{9 ( x - 1 ) ^{\frac{4}{3}}}

x \to 0 + lim (5 sin (x) ln (x))

\frac{\partial}{\partial x} (7 e^{x^{7} y})

\frac{d}{d x} (\frac{1}{2 x} + \frac{1}{6 x ^{\frac{5}{6}}})

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

\frac{d}{d x} (e^{5 x} \cdot 5)

What is (\partial)/(\partial x)((2(y^2-4))/(3(x-1)^{1/3)}) ?
The answer to (\partial)/(\partial x)((2(y^2-4))/(3(x-1)^{1/3)}) is -(2(y^2-4))/(9(x-1)^{4/3)}