What is the derivative of sqrt(x+y) ?

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

What is the first derivative of sqrt(x+y) ?

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1 + \frac{d y}{d x}}{2 x + y}

1.24 \cdot 1 0^{- 3}

e^{- x} \cdot x^{2}

e^{- 2 l n (l n (x))}

e^{- l n (s i n (x) s i n (y))}

e^{- 1090}

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