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Popular >

(1/(sqrt(x^2+1)))^'

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

= - \frac{1}{2 ( x ^{2} + 1 ) ^{\frac{3}{2}}} (x^{2} + 1)^{'}

(x^{2} + 1)^{'} = 2 x

= - \frac{1}{2 ( x ^{2} + 1 ) ^{\frac{3}{2}}} \cdot 2 x

Simplify

- \frac{1}{2 ( x ^{2} + 1 ) ^{\frac{3}{2}}} \cdot 2 x : - \frac{x}{( x ^{2} + 1 ) ^{\frac{3}{2}}}

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

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Frequently Asked Questions (FAQ)

What is the (1/(sqrt(x^2+1)))^' ?
The (1/(sqrt(x^2+1)))^' is -x/((x^2+1)^{3/2)}
What is the first (1/(sqrt(x^2+1)))^' ?
The first (1/(sqrt(x^2+1)))^' is -x/((x^2+1)^{3/2)}