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}}}

\int 5 x arctan (x) d x

\frac{\partial}{\partial y} ((e^{x} - 4 x) cos (y))

\int \frac{1}{x} + \frac{y ^{2}}{x ^{2}} d x

\frac{d}{d x} (ln ((x - 1)^{3} (x^{2} + 1)^{4}))

\frac{d}{d x} (3 x^{2} - e^{2 x})

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}}