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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derivative of

(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}}}

(x^{2} + 49) \frac{d y}{d x} = 7

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

\int \frac{x ^{8}}{x ^{3} + 2} d x

4 x^{4} + 3 x^{3} + 2 x^{2} + x + 1, 1

\frac{\partial}{\partial x} (- 5 y e^{x})

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)}