What is (\partial)/(\partial x)(5y^{1/4}x^{1/2}) ?

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

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(\partial)/(\partial x)(5y^{1/4}x^{1/2})

\frac{\partial}{\partial x} (5 y^{\frac{1}{4}} x^{\frac{1}{2}})

\frac{5 y ^{\frac{1}{4}}}{2 x ^{\frac{1}{2}}}

Solution steps

\frac{\partial}{\partial x} (5 y^{\frac{1}{4}} x^{\frac{1}{2}})

Treat

y

as a constant

Take the constant out:

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

= 5 y^{\frac{1}{4}} \frac{\partial}{\partial x} (x^{\frac{1}{2}})

Apply the Power Rule:

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

= 5 y^{\frac{1}{4}} \frac{1}{2} x^{\frac{1}{2} - 1}

Simplify

5 y^{\frac{1}{4}} \frac{1}{2} x^{\frac{1}{2} - 1} : \frac{5 y ^{\frac{1}{4}}}{2 x ^{\frac{1}{2}}}

= \frac{5 y ^{\frac{1}{4}}}{2 x ^{\frac{1}{2}}}

\int x^{3} 4 + x^{4} d x

\frac{d y}{d x} = y (3 - y)

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

\frac{d}{d x} (+ 2 x)

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