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

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

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

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

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derivative of

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

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

Solution steps

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

Simplify

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

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

Take the constant out:

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

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int sin (20 x) sin (21 x) d x

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

\frac{d}{d x} (\frac{4 x ^{2} + 5}{x ^{2} + 7})

\frac{\partial}{\partial y} (10 - 6 y + e^{- 3 x})

\frac{d}{d t} (3 e^{t})

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