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

The derivative of ((x)/(sqrt(x^2+1))) is 1/((x^2+1)sqrt(x^2+1))

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

\frac{d}{d x} (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}

x \to x lim (x)

y = (5 x - 1) (4 + 3 x) x, at x = 0

n = 1 \sum \infty \frac{7}{3 ^{n}}

\frac{d}{d x} (x^{2} + \frac{16}{x})

y^{^{''}} + 2 y^{^{'}} + 5 y = 0, y (0) = 1, y^{^{'}} (0) = 1

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