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

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

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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \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}}

= 2 \cdot \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

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

Simplify

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

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

(1, 4), (- 1, - 4)

\int sin (x) sin (x + \frac{π}{6}) d x

\frac{\partial}{\partial x} (6 x^{2} cos (y^{7}))

y = \frac{8 x ^{2} + 6 x + 2}{x}

\int_{1}^{5} 5 d x

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