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

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

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

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

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derivative of

\frac{200}{t + 2}

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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