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Popular >

derivative of x/(x^2+3)

Solution

derivative of

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

Solution

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

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) = 2 x

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

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

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

Popular Examples

integral of cos^2(xsi)n^3x

\int cos^{2} (x s i) n^{3} x d x

tangent of e^{-2t},\at t=0 tangent of

e^{- 2 t}, at t = 0

derivative of (sqrt(x)/(x-2sqrt(x)))

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

limit as x approaches-1 of 2x^2+6x-1

x \to - 1 lim (2 x^{2} + 6 x - 1)

limit as x approaches 2 of 5/(|2-x|)

x \to 2 lim (\frac{5}{∣ 2 - x ∣})

Frequently Asked Questions (FAQ)

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