What is (\partial)/(\partial x)(25x^{(3/4)}y^{1/4}) ?

The answer to (\partial)/(\partial x)(25x^{(3/4)}y^{1/4}) is (75y^{1/4})/(4x^{1/4)}

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(\partial)/(\partial x)(25x^{(3/4)}y^{1/4})

\frac{\partial}{\partial x} (25 x^{(\frac{3}{4})} y^{\frac{1}{4}})

\frac{75 y ^{\frac{1}{4}}}{4 x ^{\frac{1}{4}}}

Solution steps

\frac{\partial}{\partial x} (25 x^{(\frac{3}{4})} y^{\frac{1}{4}})

Treat

y

as a constant

Take the constant out:

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

= 25 y^{\frac{1}{4}} \frac{\partial}{\partial x} (x^{\frac{3}{4}})

Apply the Power Rule:

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

= 25 y^{\frac{1}{4}} \frac{3}{4} x^{\frac{3}{4} - 1}

Simplify

25 y^{\frac{1}{4}} \frac{3}{4} x^{\frac{3}{4} - 1} : \frac{75 y ^{\frac{1}{4}}}{4 x ^{\frac{1}{4}}}

= \frac{75 y ^{\frac{1}{4}}}{4 x ^{\frac{1}{4}}}

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What is (\partial)/(\partial x)(25x^{(3/4)}y^{1/4}) ?
The answer to (\partial)/(\partial x)(25x^{(3/4)}y^{1/4}) is (75y^{1/4})/(4x^{1/4)}