What is the derivative of 4/((x+1^2)) ?

The derivative of 4/((x+1^2)) is -8/((x+1)^3)

What is the first derivative of 4/((x+1^2)) ?

The first derivative of 4/((x+1^2)) is -8/((x+1)^3)

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

- \frac{8}{( x + 1 ) ^{3}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

4 (- \frac{2}{( x + 1 ) ^{3}} \cdot 1) : - \frac{8}{( x + 1 ) ^{3}}

= - \frac{8}{( x + 1 ) ^{3}}

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

y = \frac{2}{x}

\int x^{\frac{1}{2}} 1 + x^{\frac{1}{2}} d x

\int 1 0^{2 x} d x

x \to 0 lim (x + 3)

What is the derivative of 4/((x+1^2)) ?
The derivative of 4/((x+1^2)) is -8/((x+1)^3)
What is the first derivative of 4/((x+1^2)) ?
The first derivative of 4/((x+1^2)) is -8/((x+1)^3)