What is (\partial)/(\partial y)((x-5)^{1/4}y^{1/4}) ?

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

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(\partial)/(\partial y)((x-5)^{1/4}y^{1/4})

\frac{\partial}{\partial y} ((x - 5)^{\frac{1}{4}} y^{\frac{1}{4}})

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

Solution steps

\frac{\partial}{\partial y} ((x - 5)^{\frac{1}{4}} y^{\frac{1}{4}})

Treat

x

as a constant

Take the constant out:

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

= (x - 5)^{\frac{1}{4}} \frac{\partial}{\partial y} (y^{\frac{1}{4}})

Apply the Power Rule:

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

= (x - 5)^{\frac{1}{4}} \frac{1}{4} y^{\frac{1}{4} - 1}

Simplify

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

= \frac{( x - 5 ) ^{\frac{1}{4}}}{4 y ^{\frac{3}{4}}}

\frac{d}{d x} (x^{x + 1})

\frac{d}{d x} (- e^{- x y})

\int_{1}^{\infty} (e^{- x}) d x

\int \frac{6}{x - 1} d x

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