What is the derivative of-(2x/((9+x^2)^2)) ?

The derivative of-(2x/((9+x^2)^2)) is -(6(-x^2+3))/((9+x^2)^3)

What is the first derivative of-(2x/((9+x^2)^2)) ?

The first derivative of-(2x/((9+x^2)^2)) is -(6(-x^2+3))/((9+x^2)^3)

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

- \frac{6 ( - x ^{2} + 3 )}{( 9 + x ^{2} ) ^{3}}

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} ((9 + x^{2})^{2}) = 4 x (9 + x^{2})

= - 2 \cdot \frac{1 \cdot ( 9 + x ^{2} ) ^{2} - 4 x ( 9 + x ^{2} ) x}{( ( 9 + x ^{2} ) ^{2} ) ^{2}}

Simplify

- 2 \cdot \frac{1 \cdot ( 9 + x ^{2} ) ^{2} - 4 x ( 9 + x ^{2} ) x}{( ( 9 + x ^{2} ) ^{2} ) ^{2}} : - \frac{6 ( - x ^{2} + 3 )}{( 9 + x ^{2} ) ^{3}}

= - \frac{6 ( - x ^{2} + 3 )}{( 9 + x ^{2} ) ^{3}}

\frac{d x}{d t} = 12 - \frac{x}{200 + 3 t}

f (x) = x^{3} - 3 x^{2} - 9 x + 27, at x = 4

\frac{\partial}{\partial x} (\frac{3 x + y ^{2}}{x y})

\int (5 x^{4} - 8 x^{3} + 9 x^{2} - 2 x + 7) d x

y^{^{'}} = y^{5}

What is the derivative of-(2x/((9+x^2)^2)) ?
The derivative of-(2x/((9+x^2)^2)) is -(6(-x^2+3))/((9+x^2)^3)
What is the first derivative of-(2x/((9+x^2)^2)) ?
The first derivative of-(2x/((9+x^2)^2)) is -(6(-x^2+3))/((9+x^2)^3)