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Popular >

derivative of f(x)= x/(x^2-9)

Solution

derivative of

f (x) = \frac{x}{x ^{2} - 9}

Solution

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

Solution steps

\frac{d}{d x} (\frac{x}{x ^{2} - 9})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( x ^{2} - 9 ) - \frac{d}{d x} ( x ^{2} - 9 ) x}{( x ^{2} - 9 ) ^{2}}

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

\frac{d}{d x} (x^{2} - 9) = 2 x

= \frac{1 \cdot ( x ^{2} - 9 ) - 2 xx}{( x ^{2} - 9 ) ^{2}}

1 \cdot (x^{2} - 9) - 2 xx = - x^{2} - 9

= \frac{- x ^{2} - 9}{( x ^{2} - 9 ) ^{2}}

Popular Examples

tangent of y=x^2+5x+6,\at x=7 tangent of

y = x^{2} + 5 x + 6, at x = 7

integral of sqrt(144-9x^2)

\int 144 - 9 x^{2} d x

limit as x approaches-5+of 3/(x^2-25)

x \to - 5 + lim (\frac{3}{x ^{2} - 25})

derivative of x^{sin(3x})

\frac{d}{d x} (x^{s i n (3 x)})

(\partial)/(\partial u)(cos(u+v))

\frac{\partial}{\partial u} (cos (u + v))

Frequently Asked Questions (FAQ)

What is the derivative of f(x)= x/(x^2-9) ?
The derivative of f(x)= x/(x^2-9) is (-x^2-9)/((x^2-9)^2)
What is the first derivative of f(x)= x/(x^2-9) ?
The first derivative of f(x)= x/(x^2-9) is (-x^2-9)/((x^2-9)^2)