What is (\partial)/(\partial x)(30x^{3/4}y^{1/4}) ?

The answer to (\partial)/(\partial x)(30x^{3/4}y^{1/4}) is (45y^{1/4})/(2x^{1/4)}

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(\partial)/(\partial x)(30x^{3/4}y^{1/4})

\frac{\partial}{\partial x} (30 x^{\frac{3}{4}} y^{\frac{1}{4}})

\frac{45 y ^{\frac{1}{4}}}{2 x ^{\frac{1}{4}}}

Solution steps

\frac{\partial}{\partial x} (30 x^{\frac{3}{4}} y^{\frac{1}{4}})

Treat

y

as a constant

Take the constant out:

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

= 30 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}

= 30 y^{\frac{1}{4}} \frac{3}{4} x^{\frac{3}{4} - 1}

Simplify

30 y^{\frac{1}{4}} \frac{3}{4} x^{\frac{3}{4} - 1} : \frac{45 y ^{\frac{1}{4}}}{2 x ^{\frac{1}{4}}}

= \frac{45 y ^{\frac{1}{4}}}{2 x ^{\frac{1}{4}}}

\frac{d}{d x} (\frac{9 + 2 x - 4 x}{x})

\int 5 x e^{- 5 x} d x

\int (\frac{y}{1 + y ^{2}}) d y

f (x) = 12 sin (\frac{π t}{4})

\frac{d y}{d x} - \frac{y}{x} = 1

What is (\partial)/(\partial x)(30x^{3/4}y^{1/4}) ?
The answer to (\partial)/(\partial x)(30x^{3/4}y^{1/4}) is (45y^{1/4})/(2x^{1/4)}