What is the derivative of-25(x/(x^2+1)) ?

The derivative of-25(x/(x^2+1)) is -(25(-x^2+1))/((x^2+1)^2)

What is the first derivative of-25(x/(x^2+1)) ?

The first derivative of-25(x/(x^2+1)) is -(25(-x^2+1))/((x^2+1)^2)

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\frac{d}{d x} (- 25 (\frac{x}{x ^{2} + 1}))

- \frac{25 ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (- 25 (\frac{x}{x ^{2} + 1}))

Simplify

- 25 (\frac{x}{x ^{2} + 1}) : - \frac{25 x}{x ^{2} + 1}

= \frac{d}{d x} (- \frac{25 x}{x ^{2} + 1})

Take the constant out:

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

= - 25 \frac{d}{d x} (\frac{x}{x ^{2} + 1})

Apply the Quotient Rule:

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

= - 25 \cdot \frac{\frac{d x}{d x} ( x ^{2} + 1 ) - \frac{d}{d x} ( x ^{2} + 1 ) x}{( x ^{2} + 1 ) ^{2}}

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

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

= - 25 \cdot \frac{1 \cdot ( x ^{2} + 1 ) - 2 xx}{( x ^{2} + 1 ) ^{2}}

Simplify

- 25 \cdot \frac{1 \cdot ( x ^{2} + 1 ) - 2 xx}{( x ^{2} + 1 ) ^{2}} : - \frac{25 ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{2}}

= - \frac{25 ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{2}}

\int (8 x + 9) d x

\int cos (9 x) d x

\int cot (\frac{1}{8} x) d x

\frac{d}{d x} (\frac{4 x ^{\frac{3}{2}} - x ^{3} + 8}{x})

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

What is the derivative of-25(x/(x^2+1)) ?
The derivative of-25(x/(x^2+1)) is -(25(-x^2+1))/((x^2+1)^2)
What is the first derivative of-25(x/(x^2+1)) ?
The first derivative of-25(x/(x^2+1)) is -(25(-x^2+1))/((x^2+1)^2)