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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

y = \frac{t}{( t - 1 ) ^{2}}

f (x) = \frac{4}{5 x + 1}, at x = - 1

(ln (sin (x)))^{^{'}}

\frac{\partial}{\partial x} ((1 x, 3 y, 4 z) \cdot (1, 2, 3))

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