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Popular Calculus >

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

Solution

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

Solution

\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}

Graph

Popular Examples

derivative of (cot(x)/(sin(x)))

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

derivative of x^3+x^2-x

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

limit as x approaches-2 of (-9)/(x^2)

x \to - 2 lim (\frac{- 9}{x ^{2}})

limit as x approaches infinity of (5)\sqrt[6666]{6}

x \to \infty lim ((5) 66666)

y^{''}+6y^'+25y=100,y(0)=0,y^'(0)=0

y^{^{''}} + 6 y^{^{'}} + 25 y = 100, y (0) = 0, y^{^{'}} (0) = 0

Frequently Asked Questions (FAQ)

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))