What is (\partial)/(\partial x)(L+(L^2+x^2)^{1/2}) ?

The answer to (\partial)/(\partial x)(L+(L^2+x^2)^{1/2}) is x/((x^2+L^2)^{1/2)}

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(\partial)/(\partial x)(L+(L^2+x^2)^{1/2})

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

\frac{x}{( x ^{2} + L ^{2} ) ^{\frac{1}{2}}}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial x} (L) = 0

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

= 0 + \frac{x}{( L ^{2} + x ^{2} ) ^{\frac{1}{2}}}

Simplify

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

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What is (\partial)/(\partial x)(L+(L^2+x^2)^{1/2}) ?
The answer to (\partial)/(\partial x)(L+(L^2+x^2)^{1/2}) is x/((x^2+L^2)^{1/2)}