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}}}

\frac{d}{d x} (sin (3 x^{2}) + 2 x^{3})

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

\int (sin (3 x)) d x

\frac{\partial}{\partial x} (6 cos^{4} (3 x + 2))

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

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)}