What is the derivative of (x^2+y^2^{1/2}) ?

The derivative of (x^2+y^2^{1/2}) is (x+y\frac{dy)/(dx)}{(x^2+y^2)^{1/2}}

What is the first derivative of (x^2+y^2^{1/2}) ?

The first derivative of (x^2+y^2^{1/2}) is (x+y\frac{dy)/(dx)}{(x^2+y^2)^{1/2}}

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\frac{d}{d x} ((x^{2} + y^{2})^{\frac{1}{2}})

\frac{x + y \frac{d y}{d x}}{( x ^{2} + y ^{2} ) ^{\frac{1}{2}}}

Solution steps

\frac{d}{d x} ((x^{2} + y^{2})^{\frac{1}{2}})

Apply the chain rule:

\frac{1}{2 ( x ^{2} + y ^{2} ) ^{\frac{1}{2}}} \frac{d}{d x} (x^{2} + y^{2})

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

\frac{d}{d x} (x^{2} + y^{2}) = 2 x + 2 y \frac{d y}{d x}

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

Simplify

\frac{1}{2 ( x ^{2} + y ^{2} ) ^{\frac{1}{2}}} (2 x + 2 y \frac{d y}{d x}) : \frac{x + y \frac{d y}{d x}}{( x ^{2} + y ^{2} ) ^{\frac{1}{2}}}

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

What is the derivative of (x^2+y^2^{1/2}) ?
The derivative of (x^2+y^2^{1/2}) is (x+y\frac{dy)/(dx)}{(x^2+y^2)^{1/2}}
What is the first derivative of (x^2+y^2^{1/2}) ?
The first derivative of (x^2+y^2^{1/2}) is (x+y\frac{dy)/(dx)}{(x^2+y^2)^{1/2}}