What is (\partial)/(\partial L)(-sqrt(2{K)^2+L^2}) ?

The answer to (\partial)/(\partial L)(-sqrt(2{K)^2+L^2}) is -L/(sqrt(2{K)^2+L^2)}

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(\partial)/(\partial L)(-sqrt(2{K)^2+L^2})

\frac{\partial}{\partial L} (- 2 K^{2} + L^{2})

- \frac{L}{2 K ^{2} + L ^{2}}

Solution steps

\frac{\partial}{\partial L} (- 2 K^{2} + L^{2})

Take the constant out:

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

= - \frac{\partial}{\partial L} (2 K^{2} + L^{2})

Apply the chain rule:

\frac{1}{2 2 K ^{2} + L ^{2}} \frac{\partial}{\partial L} (2 K^{2} + L^{2})

= \frac{1}{2 2 K ^{2} + L ^{2}} \frac{\partial}{\partial L} (2 K^{2} + L^{2})

\frac{\partial}{\partial L} (2 K^{2} + L^{2}) = 2 L

= - \frac{1}{2 2 K ^{2} + L ^{2}} \cdot 2 L

Simplify

- \frac{1}{2 2 K ^{2} + L ^{2}} \cdot 2 L : - \frac{L}{2 K ^{2} + L ^{2}}

= - \frac{L}{2 K ^{2} + L ^{2}}

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What is (\partial)/(\partial L)(-sqrt(2{K)^2+L^2}) ?
The answer to (\partial)/(\partial L)(-sqrt(2{K)^2+L^2}) is -L/(sqrt(2{K)^2+L^2)}