What is the derivative of-5/((x+3^3)) ?

The derivative of-5/((x+3^3)) is (15)/((x+3)^4)

What is the first derivative of-5/((x+3^3)) ?

The first derivative of-5/((x+3^3)) is (15)/((x+3)^4)

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

\frac{15}{( x + 3 ) ^{4}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

= - 5 (- \frac{3}{( x + 3 ) ^{4}} \cdot 1)

Simplify

- 5 (- \frac{3}{( x + 3 ) ^{4}} \cdot 1) : \frac{15}{( x + 3 ) ^{4}}

= \frac{15}{( x + 3 ) ^{4}}

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What is the derivative of-5/((x+3^3)) ?
The derivative of-5/((x+3^3)) is (15)/((x+3)^4)
What is the first derivative of-5/((x+3^3)) ?
The first derivative of-5/((x+3^3)) is (15)/((x+3)^4)