What is the derivative of x/(sqrt(x^2+3)) ?

The derivative of x/(sqrt(x^2+3)) is 3/((x^2+3)sqrt(x^2+3))

What is the first derivative of x/(sqrt(x^2+3)) ?

The first derivative of x/(sqrt(x^2+3)) is 3/((x^2+3)sqrt(x^2+3))

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\frac{d}{d x} (\frac{x}{x ^{2} + 3})

\frac{3}{( x ^{2} + 3 ) x ^{2} + 3}

Solution steps

\frac{d}{d x} (\frac{x}{x ^{2} + 3})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} x ^{2} + 3 - \frac{d}{d x} ( x ^{2} + 3 ) x}{( x ^{2} + 3 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 3) = \frac{x}{x ^{2} + 3}

= \frac{1 \cdot x ^{2} + 3 - \frac{x}{x ^{2} + 3} x}{( x ^{2} + 3 ) ^{2}}

Simplify

\frac{1 \cdot x ^{2} + 3 - \frac{x}{x ^{2} + 3} x}{( x ^{2} + 3 ) ^{2}} : \frac{3}{( x ^{2} + 3 ) x ^{2} + 3}

= \frac{3}{( x ^{2} + 3 ) x ^{2} + 3}

\int e^{8 θ} sin (9 θ) d θ

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\frac{d}{d x} (tan (2 x))

\frac{d}{d x} (\frac{cot ( x )}{sin ( x )})

\frac{d}{d x} (x^{3} + x^{2} - x)

What is the derivative of x/(sqrt(x^2+3)) ?
The derivative of x/(sqrt(x^2+3)) is 3/((x^2+3)sqrt(x^2+3))
What is the first derivative of x/(sqrt(x^2+3)) ?
The first derivative of x/(sqrt(x^2+3)) is 3/((x^2+3)sqrt(x^2+3))