What is the derivative of-(200)/((t+2)^2) ?

The derivative of-(200)/((t+2)^2) is (400)/((t+2)^3)

What is the first derivative of-(200)/((t+2)^2) ?

The first derivative of-(200)/((t+2)^2) is (400)/((t+2)^3)

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derivative of

- \frac{200}{( t + 2 ) ^{2}}

\frac{400}{( t + 2 ) ^{3}}

Solution steps

\frac{d}{d t} (- \frac{200}{( t + 2 ) ^{2}})

Take the constant out:

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

= - 200 \frac{d}{d t} (\frac{1}{( t + 2 ) ^{2}})

Apply exponent rule:

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

= - 200 \frac{d}{d t} ((t + 2)^{- 2})

Apply the chain rule:

- \frac{2}{( t + 2 ) ^{3}} \frac{d}{d t} (t + 2)

= - \frac{2}{( t + 2 ) ^{3}} \frac{d}{d t} (t + 2)

\frac{d}{d t} (t + 2) = 1

= - 200 (- \frac{2}{( t + 2 ) ^{3}} \cdot 1)

Simplify

- 200 (- \frac{2}{( t + 2 ) ^{3}} \cdot 1) : \frac{400}{( t + 2 ) ^{3}}

= \frac{400}{( t + 2 ) ^{3}}

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What is the derivative of-(200)/((t+2)^2) ?
The derivative of-(200)/((t+2)^2) is (400)/((t+2)^3)
What is the first derivative of-(200)/((t+2)^2) ?
The first derivative of-(200)/((t+2)^2) is (400)/((t+2)^3)