What is the derivative of-(2x/(5(x^2+1)^2)) ?

The derivative of-(2x/(5(x^2+1)^2)) is -(2(-3x^2+1))/(5(x^2+1)^3)

What is the first derivative of-(2x/(5(x^2+1)^2)) ?

The first derivative of-(2x/(5(x^2+1)^2)) is -(2(-3x^2+1))/(5(x^2+1)^3)

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\frac{d}{d x} (- \frac{2 x}{5 ( x ^{2} + 1 ) ^{2}})

- \frac{2 ( - 3 x ^{2} + 1 )}{5 ( x ^{2} + 1 ) ^{3}}

Solution steps

\frac{d}{d x} (- \frac{2 x}{5 ( x ^{2} + 1 ) ^{2}})

Take the constant out:

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

= - \frac{2}{5} \frac{d}{d x} (\frac{x}{( x ^{2} + 1 ) ^{2}})

Apply the Quotient Rule:

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

= - \frac{2}{5} \cdot \frac{\frac{d x}{d x} ( x ^{2} + 1 ) ^{2} - \frac{d}{d x} ( ( x ^{2} + 1 ) ^{2} ) x}{( ( x ^{2} + 1 ) ^{2} ) ^{2}}

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

\frac{d}{d x} ((x^{2} + 1)^{2}) = 4 x (x^{2} + 1)

= - \frac{2}{5} \cdot \frac{1 \cdot ( x ^{2} + 1 ) ^{2} - 4 x ( x ^{2} + 1 ) x}{( ( x ^{2} + 1 ) ^{2} ) ^{2}}

Simplify

- \frac{2}{5} \cdot \frac{1 \cdot ( x ^{2} + 1 ) ^{2} - 4 x ( x ^{2} + 1 ) x}{( ( x ^{2} + 1 ) ^{2} ) ^{2}} : - \frac{2 ( - 3 x ^{2} + 1 )}{5 ( x ^{2} + 1 ) ^{3}}

= - \frac{2 ( - 3 x ^{2} + 1 )}{5 ( x ^{2} + 1 ) ^{3}}

x \to - \infty lim (A (x))

(2 x + y + 1) \frac{d y}{d x} = 1

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

n \to \infty lim (2)

\int 6 sin^{3} (x co) s^{5} x d x

What is the derivative of-(2x/(5(x^2+1)^2)) ?
The derivative of-(2x/(5(x^2+1)^2)) is -(2(-3x^2+1))/(5(x^2+1)^3)
What is the first derivative of-(2x/(5(x^2+1)^2)) ?
The first derivative of-(2x/(5(x^2+1)^2)) is -(2(-3x^2+1))/(5(x^2+1)^3)