What is the derivative of 1/((x^4+1^3)) ?

The derivative of 1/((x^4+1^3)) is -(12x^3)/((x^4+1)^4)

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

The first derivative of 1/((x^4+1^3)) is -(12x^3)/((x^4+1)^4)

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

- \frac{12 x ^{3}}{( x ^{4} + 1 ) ^{4}}

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

- \frac{3}{( x ^{4} + 1 ) ^{4}} \cdot 4 x^{3} : - \frac{12 x ^{3}}{( x ^{4} + 1 ) ^{4}}

= - \frac{12 x ^{3}}{( x ^{4} + 1 ) ^{4}}

4.9 x^{1.9}, at x = 1.4

\frac{d}{d x} (x^{a} ln (x))

f (x) = 5 x e^{x}

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

\frac{\partial}{\partial u ( v )} (\frac{e ^{v}}{u ( v ) + v ^{4}})

What is the derivative of 1/((x^4+1^3)) ?
The derivative of 1/((x^4+1^3)) is -(12x^3)/((x^4+1)^4)
What is the first derivative of 1/((x^4+1^3)) ?
The first derivative of 1/((x^4+1^3)) is -(12x^3)/((x^4+1)^4)