What is the derivative of f(x)= x/(9x^2-1) ?

The derivative of f(x)= x/(9x^2-1) is (-9x^2-1)/((9x^2-1)^2)

What is the first derivative of f(x)= x/(9x^2-1) ?

The first derivative of f(x)= x/(9x^2-1) is (-9x^2-1)/((9x^2-1)^2)

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derivative of

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

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

Solution steps

\frac{d}{d x} (\frac{x}{9 x ^{2} - 1})

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (9 x^{2} - 1) = 18 x

= \frac{1 \cdot ( 9 x ^{2} - 1 ) - 18 xx}{( 9 x ^{2} - 1 ) ^{2}}

1 \cdot (9 x^{2} - 1) - 18 xx = - 9 x^{2} - 1

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

\frac{d}{d x} (ln (\frac{x + 3}{x - 3}))

x \to 0 + lim (\frac{x}{15 x ^{4} + 12 x})

x \to 2 lim (\frac{x ^{2} - 4}{x - 3})

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

6 t

What is the derivative of f(x)= x/(9x^2-1) ?
The derivative of f(x)= x/(9x^2-1) is (-9x^2-1)/((9x^2-1)^2)
What is the first derivative of f(x)= x/(9x^2-1) ?
The first derivative of f(x)= x/(9x^2-1) is (-9x^2-1)/((9x^2-1)^2)