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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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