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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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