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Popular >

derivative of x/(sqrt(x^2+1)-1)

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (1) = 0

= \frac{1}{( x ^{2} + 1 ) x ^{2} + 1} - 0

Simplify

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

Popular Examples

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\int \frac{1}{18} x d x

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x \to 1 lim (∣ x + 1 ∣)

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\int \frac{( e ^{- \frac{1}{x}} )}{x ^{2}} d x

Frequently Asked Questions (FAQ)

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