What is the (x/(sqrt(x^2+1)))^' ?

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

What is the first (x/(sqrt(x^2+1)))^' ?

The first (x/(sqrt(x^2+1)))^' is 1/((x^2+1)sqrt(x^2+1))

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

x^{'} = 1

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

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

Simplify

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

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

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