What is (\partial)/(\partial x)(6x^{1/3}y^{2/3}) ?

The answer to (\partial)/(\partial x)(6x^{1/3}y^{2/3}) is (2y^{2/3})/(x^{2/3)}

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(\partial)/(\partial x)(6x^{1/3}y^{2/3})

\frac{\partial}{\partial x} (6 x^{\frac{1}{3}} y^{\frac{2}{3}})

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

Solution steps

\frac{\partial}{\partial x} (6 x^{\frac{1}{3}} y^{\frac{2}{3}})

Treat

y

as a constant

Take the constant out:

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

= 6 y^{\frac{2}{3}} \frac{\partial}{\partial x} (x^{\frac{1}{3}})

Apply the Power Rule:

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

= 6 y^{\frac{2}{3}} \frac{1}{3} x^{\frac{1}{3} - 1}

Simplify

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

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

\frac{d}{d a} (\frac{cos ^{2} ( a )}{sin ( a ) - 1})

f (x) = x^{4} + 4 x^{2} - x, (1, 4)

\int \frac{x ^{2}}{x ^{2} + 16} d x

n = 1 \sum \infty \frac{1000}{5 ^{n}}

5 + 4 e^{- 2 t}

What is (\partial)/(\partial x)(6x^{1/3}y^{2/3}) ?
The answer to (\partial)/(\partial x)(6x^{1/3}y^{2/3}) is (2y^{2/3})/(x^{2/3)}