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

The answer to (\partial)/(\partial y)(10x^{1/4}y^{3/4}) is (15x^{1/4})/(2y^{1/4)}

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

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

\frac{15 x ^{\frac{1}{4}}}{2 y ^{\frac{1}{4}}}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

= 10 x^{\frac{1}{4}} \frac{3}{4} y^{\frac{3}{4} - 1}

Simplify

10 x^{\frac{1}{4}} \frac{3}{4} y^{\frac{3}{4} - 1} : \frac{15 x ^{\frac{1}{4}}}{2 y ^{\frac{1}{4}}}

= \frac{15 x ^{\frac{1}{4}}}{2 y ^{\frac{1}{4}}}

n = 1 \sum \infty \frac{1}{n + e ^{n}}

n = 0 \sum \infty (1)^{n}

f (x) = 3 x^{2} - 4

\frac{\partial}{\partial y} (yz ln (x y))

\frac{\partial}{\partial x} (sin (π (5 x - 6 y)))

What is (\partial)/(\partial y)(10x^{1/4}y^{3/4}) ?
The answer to (\partial)/(\partial y)(10x^{1/4}y^{3/4}) is (15x^{1/4})/(2y^{1/4)}