What is the derivative of-(25/((1+5x)^2)) ?

The derivative of-(25/((1+5x)^2)) is (250)/((1+5x)^3)

What is the first derivative of-(25/((1+5x)^2)) ?

The first derivative of-(25/((1+5x)^2)) is (250)/((1+5x)^3)

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\frac{d}{d x} (- \frac{25}{( 1 + 5 x ) ^{2}})

\frac{250}{( 1 + 5 x ) ^{3}}

Solution steps

\frac{d}{d x} (- \frac{25}{( 1 + 5 x ) ^{2}})

Take the constant out:

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

= - 25 \frac{d}{d x} (\frac{1}{( 1 + 5 x ) ^{2}})

Apply exponent rule:

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

= - 25 \frac{d}{d x} ((1 + 5 x)^{- 2})

Apply the chain rule:

- \frac{2}{( 1 + 5 x ) ^{3}} \frac{d}{d x} (1 + 5 x)

= - \frac{2}{( 1 + 5 x ) ^{3}} \frac{d}{d x} (1 + 5 x)

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

= - 25 (- \frac{2}{( 1 + 5 x ) ^{3}} \cdot 5)

Simplify

- 25 (- \frac{2}{( 1 + 5 x ) ^{3}} \cdot 5) : \frac{250}{( 1 + 5 x ) ^{3}}

= \frac{250}{( 1 + 5 x ) ^{3}}

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What is the derivative of-(25/((1+5x)^2)) ?
The derivative of-(25/((1+5x)^2)) is (250)/((1+5x)^3)
What is the first derivative of-(25/((1+5x)^2)) ?
The first derivative of-(25/((1+5x)^2)) is (250)/((1+5x)^3)