What is (\partial)/(\partial x)(x^{1/8}*y^{11/9}) ?

The answer to (\partial)/(\partial x)(x^{1/8}*y^{11/9}) is (y^{11/9})/(8x^{7/8)}

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(\partial)/(\partial x)(x^{1/8}*y^{11/9})

\frac{\partial}{\partial x} (x^{\frac{1}{8}} \cdot y^{\frac{11}{9}})

\frac{y ^{\frac{11}{9}}}{8 x ^{\frac{7}{8}}}

Solution steps

\frac{\partial}{\partial x} (x^{\frac{1}{8}} y^{\frac{11}{9}})

Treat

y

as a constant

Take the constant out:

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

= y^{\frac{11}{9}} \frac{\partial}{\partial x} (x^{\frac{1}{8}})

Apply the Power Rule:

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

= y^{\frac{11}{9}} \frac{1}{8} x^{\frac{1}{8} - 1}

Simplify

y^{\frac{11}{9}} \frac{1}{8} x^{\frac{1}{8} - 1} : \frac{y ^{\frac{11}{9}}}{8 x ^{\frac{7}{8}}}

= \frac{y ^{\frac{11}{9}}}{8 x ^{\frac{7}{8}}}

\int \frac{x ^{5}}{( 1 - x ^{3} ) ^{\frac{3}{2}}} d x

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

(x - y) d x - x d y = 0

\int x^{3} x^{2} + 3 d x

\int_{0}^{1} \frac{x - 1}{x + 1} d x

What is (\partial)/(\partial x)(x^{1/8}*y^{11/9}) ?
The answer to (\partial)/(\partial x)(x^{1/8}*y^{11/9}) is (y^{11/9})/(8x^{7/8)}