What is the derivative of 1/(x^4*(5-x)) ?

The derivative of 1/(x^4*(5-x)) is -(5(-x+4))/(x^5(-x+5)^2)

What is the first derivative of 1/(x^4*(5-x)) ?

The first derivative of 1/(x^4*(5-x)) is -(5(-x+4))/(x^5(-x+5)^2)

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\frac{d}{d x} (\frac{1}{x ^{4} \cdot ( 5 - x )})

- \frac{5 ( - x + 4 )}{x ^{5} ( - x + 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{x ^{4} ( 5 - x )})

Apply exponent rule:

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

= \frac{d}{d x} ((x^{4} (5 - x))^{- 1})

Apply the chain rule:

- \frac{1}{( x ^{4} ( 5 - x ) ) ^{2}} \frac{d}{d x} (x^{4} (5 - x))

= - \frac{1}{( x ^{4} ( 5 - x ) ) ^{2}} \frac{d}{d x} (x^{4} (5 - x))

\frac{d}{d x} (x^{4} (5 - x)) = 20 x^{3} - 5 x^{4}

= - \frac{1}{( x ^{4} ( 5 - x ) ) ^{2}} (20 x^{3} - 5 x^{4})

Simplify

- \frac{1}{( x ^{4} ( 5 - x ) ) ^{2}} (20 x^{3} - 5 x^{4}) : - \frac{5 ( - x + 4 )}{x ^{5} ( - x + 5 ) ^{2}}

= - \frac{5 ( - x + 4 )}{x ^{5} ( - x + 5 ) ^{2}}

What is the derivative of 1/(x^4*(5-x)) ?
The derivative of 1/(x^4*(5-x)) is -(5(-x+4))/(x^5(-x+5)^2)
What is the first derivative of 1/(x^4*(5-x)) ?
The first derivative of 1/(x^4*(5-x)) is -(5(-x+4))/(x^5(-x+5)^2)