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

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

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

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

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{6 x ^{2}}{( x ^{3} + 4 ) ^{3}}

x \to 0 - lim (x ln (x))

\int_{3}^{8} (x^{3} - π x^{2}) d x

n = 0 \sum \infty 9 ((\frac{5}{12})^{n})

\int \frac{x ^{6} e ^{x}}{x} d x

\frac{d y}{d x} + 3 x^{2} y = 6 x^{2}

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