What is (\partial)/(\partial x)(10x^{1/4}*2y^{3/4}) ?

The answer to (\partial)/(\partial x)(10x^{1/4}*2y^{3/4}) is (5y^{3/4})/(x^{3/4)}

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(\partial)/(\partial x)(10x^{1/4}*2y^{3/4})

\frac{\partial}{\partial x} (10 x^{\frac{1}{4}} \cdot 2 y^{\frac{3}{4}})

\frac{5 y ^{\frac{3}{4}}}{x ^{\frac{3}{4}}}

Solution steps

\frac{\partial}{\partial x} (10 x^{\frac{1}{4}} \cdot 2 y^{\frac{3}{4}})

Simplify

10 x^{\frac{1}{4}} \cdot 2 y^{\frac{3}{4}} : 20 x^{\frac{1}{4}} y^{\frac{3}{4}}

= \frac{\partial}{\partial x} (20 x^{\frac{1}{4}} y^{\frac{3}{4}})

Treat

y

as a constant

Take the constant out:

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

= 20 y^{\frac{3}{4}} \frac{\partial}{\partial x} (x^{\frac{1}{4}})

Apply the Power Rule:

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

= 20 y^{\frac{3}{4}} \frac{1}{4} x^{\frac{1}{4} - 1}

Simplify

20 y^{\frac{3}{4}} \frac{1}{4} x^{\frac{1}{4} - 1} : \frac{5 y ^{\frac{3}{4}}}{x ^{\frac{3}{4}}}

= \frac{5 y ^{\frac{3}{4}}}{x ^{\frac{3}{4}}}

x \to 1 lim (4 x^{2} - 2 x - 6)

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

sec^{5} (x)

\int_{1200}^{1210} x \cdot 0.1 d x

(\frac{4 x ^{3} + 5}{- 5 x ^{2} + 1})^{\frac{1}{4}}

What is (\partial)/(\partial x)(10x^{1/4}*2y^{3/4}) ?
The answer to (\partial)/(\partial x)(10x^{1/4}*2y^{3/4}) is (5y^{3/4})/(x^{3/4)}