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

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

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

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

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derivative of

\frac{200 t}{t + 2}

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d t}{d t} = 1

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

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

Simplify

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

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

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