What is the derivative of (2x+5^{1/2}) ?

The derivative of (2x+5^{1/2}) is 1/((2x+5)^{1/2)}

What is the first derivative of (2x+5^{1/2}) ?

The first derivative of (2x+5^{1/2}) is 1/((2x+5)^{1/2)}

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\frac{d}{d x} ((2 x + 5)^{\frac{1}{2}})

\frac{1}{( 2 x + 5 ) ^{\frac{1}{2}}}

Solution steps

\frac{d}{d x} ((2 x + 5)^{\frac{1}{2}})

Apply the chain rule:

\frac{1}{2 ( 2 x + 5 ) ^{\frac{1}{2}}} \frac{d}{d x} (2 x + 5)

= \frac{1}{2 ( 2 x + 5 ) ^{\frac{1}{2}}} \frac{d}{d x} (2 x + 5)

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

= \frac{1}{2 ( 2 x + 5 ) ^{\frac{1}{2}}} \cdot 2

Simplify

\frac{1}{2 ( 2 x + 5 ) ^{\frac{1}{2}}} \cdot 2 : \frac{1}{( 2 x + 5 ) ^{\frac{1}{2}}}

= \frac{1}{( 2 x + 5 ) ^{\frac{1}{2}}}

What is the derivative of (2x+5^{1/2}) ?
The derivative of (2x+5^{1/2}) is 1/((2x+5)^{1/2)}
What is the first derivative of (2x+5^{1/2}) ?
The first derivative of (2x+5^{1/2}) is 1/((2x+5)^{1/2)}