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

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

Popular >

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

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

\frac{2 y ^{\frac{1}{3}}}{x ^{\frac{1}{3}}}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

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

Simplify

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

= \frac{2 y ^{\frac{1}{3}}}{x ^{\frac{1}{3}}}

\int_{0}^{0.5} 150 x d x

\int_{0}^{1} \frac{29}{4 y - 1} d y

x \to 0 lim (3 x^{2} - 1)

y = 2 x^{4} + 3 x - 3

\frac{d}{d x} (2 + cos (2 x))

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