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)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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} (\frac{sec ( x )}{8 + sec ( x )})

d er i v a t i v e f (x) = - csc (x) cot (x)

\frac{d}{d x} (cos (k x))

\int \frac{1 + sin ( x )}{sec ( x )} d x

(x^{3} + 2)^{^{'}}

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)