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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

x \to 4 + lim (\frac{7}{( x - 4 ) ^{2}})

\frac{d}{d y} ((cos (x) + sin (y))^{y s i n (2 x - y)})

2 x ln (x + 1)

y = \frac{200}{0.9 + 0.1 e ^{2 x}}

x \to 0 lim (\frac{2}{x ^{2} + x})

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