What is (\partial}{\partial L}(L^{1/4)/K ^{1/4}) ?

The answer to (\partial}{\partial L}(L^{1/4)/K ^{1/4}) is ({K}^{1/4})/(4L^{3/4)}

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(\partial}{\partial L}(L^{1/4)/K ^{1/4})

\frac{\partial}{\partial L} (L^{\frac{1}{4}} K^{\frac{1}{4}})

\frac{K ^{\frac{1}{4}}}{4 L ^{\frac{3}{4}}}

Solution steps

\frac{\partial}{\partial L} (L^{\frac{1}{4}} K^{\frac{1}{4}})

Take the constant out:

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

= K^{\frac{1}{4}} \frac{\partial}{\partial L} (L^{\frac{1}{4}})

Apply the Power Rule:

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

= K^{\frac{1}{4}} \frac{1}{4} L^{\frac{1}{4} - 1}

Simplify

K^{\frac{1}{4}} \frac{1}{4} L^{\frac{1}{4} - 1} : \frac{K ^{\frac{1}{4}}}{4 L ^{\frac{3}{4}}}

= \frac{K ^{\frac{1}{4}}}{4 L ^{\frac{3}{4}}}

What is (\partial}{\partial L}(L^{1/4)/K ^{1/4}) ?
The answer to (\partial}{\partial L}(L^{1/4)/K ^{1/4}) is ({K}^{1/4})/(4L^{3/4)}