What is the derivative of 1/((x^2+1^3)) ?

The derivative of 1/((x^2+1^3)) is -(6x)/((x^2+1)^4)

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

The first derivative of 1/((x^2+1^3)) is -(6x)/((x^2+1)^4)

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

- \frac{6 x}{( x ^{2} + 1 ) ^{4}}

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{6 x}{( x ^{2} + 1 ) ^{4}}

\int \frac{e ^{3 x}}{e ^{3 x} + 9} d x

\int_{0}^{1} π (6 - \frac{3}{2} x)^{2} d x

\frac{2}{s ^{2} + s}

y^{^{''}} + 9 y = 3 cos (2 x) + 3

\int 9 - x^{2} (- 2 x) d x

What is the derivative of 1/((x^2+1^3)) ?
The derivative of 1/((x^2+1^3)) is -(6x)/((x^2+1)^4)
What is the first derivative of 1/((x^2+1^3)) ?
The first derivative of 1/((x^2+1^3)) is -(6x)/((x^2+1)^4)