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}}}

\int ln^{5} (x) d x

x \to 10 + lim (\frac{1}{( x - 10 ) ^{2}})

\int_{- 5}^{5} (x - 25 - x^{2}) d x

\frac{d}{d x} (\frac{1}{3 + ( 2 x + 1 ) ^{2}})

cos (t) y^{^{'}} + sin (t) y - 1 = 0

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)}