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Popular >

derivative of f(x)= x/(x^2-6)

Solution

derivative of

f (x) = \frac{x}{x ^{2} - 6}

Solution

\frac{- x ^{2} - 6}{( x ^{2} - 6 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{x ^{2} - 6})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( x ^{2} - 6 ) - \frac{d}{d x} ( x ^{2} - 6 ) x}{( x ^{2} - 6 ) ^{2}}

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

\frac{d}{d x} (x^{2} - 6) = 2 x

= \frac{1 \cdot ( x ^{2} - 6 ) - 2 xx}{( x ^{2} - 6 ) ^{2}}

1 \cdot (x^{2} - 6) - 2 xx = - x^{2} - 6

= \frac{- x ^{2} - 6}{( x ^{2} - 6 ) ^{2}}

Popular Examples

integral from-3 to 0 of-x^2-3x

\int_{- 3}^{0} - x^{2} - 3 x d x

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\int coth (x) d x

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\int \frac{t}{t ^{3}} d t

limit as x approaches 0 of x/(1-cos(x))

x \to 0 lim (\frac{x}{1 - cos ( x )})

derivative of (2cos(2x+sin(3x)+3)^2)

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

Frequently Asked Questions (FAQ)

What is the derivative of f(x)= x/(x^2-6) ?
The derivative of f(x)= x/(x^2-6) is (-x^2-6)/((x^2-6)^2)
What is the first derivative of f(x)= x/(x^2-6) ?
The first derivative of f(x)= x/(x^2-6) is (-x^2-6)/((x^2-6)^2)