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Popular Calculus >

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

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

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Frequently Asked Questions (FAQ)

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