What is the derivative of f(x)= 1/((x^3+8)^5) ?

The derivative of f(x)= 1/((x^3+8)^5) is -(15x^2)/((x^3+8)^6)

What is the first derivative of f(x)= 1/((x^3+8)^5) ?

The first derivative of f(x)= 1/((x^3+8)^5) is -(15x^2)/((x^3+8)^6)

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derivative of

f (x) = \frac{1}{( x ^{3} + 8 ) ^{5}}

- \frac{15 x ^{2}}{( x ^{3} + 8 ) ^{6}}

Solution steps

\frac{d}{d x} (\frac{1}{( x ^{3} + 8 ) ^{5}})

Apply exponent rule:

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

= \frac{d}{d x} ((x^{3} + 8)^{- 5})

Apply the chain rule:

- \frac{5}{( x ^{3} + 8 ) ^{6}} \frac{d}{d x} (x^{3} + 8)

= - \frac{5}{( x ^{3} + 8 ) ^{6}} \frac{d}{d x} (x^{3} + 8)

\frac{d}{d x} (x^{3} + 8) = 3 x^{2}

= - \frac{5}{( x ^{3} + 8 ) ^{6}} \cdot 3 x^{2}

Simplify

- \frac{5}{( x ^{3} + 8 ) ^{6}} \cdot 3 x^{2} : - \frac{15 x ^{2}}{( x ^{3} + 8 ) ^{6}}

= - \frac{15 x ^{2}}{( x ^{3} + 8 ) ^{6}}

\frac{d}{d x} (I n 3 x + 4)

\frac{s - 8}{2 s ^{2} + s + 12}

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

\frac{d}{d x} (x - sin (x) cos (x))

\int \frac{1}{2 x ^{3}} - \frac{1}{x ^{4}} d x

What is the derivative of f(x)= 1/((x^3+8)^5) ?
The derivative of f(x)= 1/((x^3+8)^5) is -(15x^2)/((x^3+8)^6)
What is the first derivative of f(x)= 1/((x^3+8)^5) ?
The first derivative of f(x)= 1/((x^3+8)^5) is -(15x^2)/((x^3+8)^6)