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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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