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

The derivative of (x+2^{1/2}) is 1/(2(x+2)^{1/2)}

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

The first derivative of (x+2^{1/2}) is 1/(2(x+2)^{1/2)}

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

\frac{\partial}{\partial x} (ln (x^{2} + y - 5))

\frac{d y}{d x} + y = 5 sin (2 x)

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

y = 2 x - x + 1, (4, 1)

y = x e^{- x^{2}}

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