What is the derivative of f(x)= x/(x^2+81) ?

The derivative of f(x)= x/(x^2+81) is (-x^2+81)/((x^2+81)^2)

What is the first derivative of f(x)= x/(x^2+81) ?

The first derivative of f(x)= x/(x^2+81) is (-x^2+81)/((x^2+81)^2)

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derivative of

f (x) = \frac{x}{x ^{2} + 81}

\frac{- x ^{2} + 81}{( x ^{2} + 81 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{x ^{2} + 81})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( x ^{2} + 81 ) - \frac{d}{d x} ( x ^{2} + 81 ) x}{( x ^{2} + 81 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 81) = 2 x

= \frac{1 \cdot ( x ^{2} + 81 ) - 2 xx}{( x ^{2} + 81 ) ^{2}}

1 \cdot (x^{2} + 81) - 2 xx = - x^{2} + 81

= \frac{- x ^{2} + 81}{( x ^{2} + 81 ) ^{2}}

\int_{0}^{1} (1 - x^{3}) d x

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

y^{^{'}} = 1 - y^{2}

(2 x - 7)^{4} (x^{2} + x + 1)^{5}

(9 z^{4} + 3 z^{2} + 1) (3 z^{3} - z)

What is the derivative of f(x)= x/(x^2+81) ?
The derivative of f(x)= x/(x^2+81) is (-x^2+81)/((x^2+81)^2)
What is the first derivative of f(x)= x/(x^2+81) ?
The first derivative of f(x)= x/(x^2+81) is (-x^2+81)/((x^2+81)^2)