What is the derivative of x/(sqrt(4+x^2)) ?

The derivative of x/(sqrt(4+x^2)) is 4/((4+x^2)sqrt(4+x^2))

What is the first derivative of x/(sqrt(4+x^2)) ?

The first derivative of x/(sqrt(4+x^2)) is 4/((4+x^2)sqrt(4+x^2))

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\frac{d}{d x} (\frac{x}{4 + x ^{2}})

\frac{4}{( 4 + x ^{2} ) 4 + x ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{4 + x ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} 4 + x ^{2} - \frac{d}{d x} ( 4 + x ^{2} ) x}{( 4 + x ^{2} ) ^{2}}

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

\frac{d}{d x} (4 + x^{2}) = \frac{x}{4 + x ^{2}}

= \frac{1 \cdot 4 + x ^{2} - \frac{x}{4 + x ^{2}} x}{( 4 + x ^{2} ) ^{2}}

Simplify

\frac{1 \cdot 4 + x ^{2} - \frac{x}{4 + x ^{2}} x}{( 4 + x ^{2} ) ^{2}} : \frac{4}{( 4 + x ^{2} ) 4 + x ^{2}}

= \frac{4}{( 4 + x ^{2} ) 4 + x ^{2}}

x \to 0 lim (\frac{sin ( 9 x )}{sin ( 3 x )})

\int - 4 e^{x} sin (4 y) d y

\int - x^{\frac{1}{2}} d x

\int \frac{x}{x ^{4} + x ^{2} + 1} d x

\frac{d}{d x} (\frac{( x ^{2} - 1 ) ^{4}}{x ^{2} + 1})

What is the derivative of x/(sqrt(4+x^2)) ?
The derivative of x/(sqrt(4+x^2)) is 4/((4+x^2)sqrt(4+x^2))
What is the first derivative of x/(sqrt(4+x^2)) ?
The first derivative of x/(sqrt(4+x^2)) is 4/((4+x^2)sqrt(4+x^2))