What is the derivative of (150t)/(t+3) ?

The derivative of (150t)/(t+3) is (450)/((t+3)^2)

What is the first derivative of (150t)/(t+3) ?

The first derivative of (150t)/(t+3) is (450)/((t+3)^2)

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derivative of

\frac{150 t}{t + 3}

\frac{450}{( t + 3 ) ^{2}}

Solution steps

\frac{d}{d t} (\frac{150 t}{t + 3})

Take the constant out:

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

= 150 \frac{d}{d t} (\frac{t}{t + 3})

Apply the Quotient Rule:

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

= 150 \cdot \frac{\frac{d t}{d t} ( t + 3 ) - \frac{d}{d t} ( t + 3 ) t}{( t + 3 ) ^{2}}

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

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

= 150 \cdot \frac{1 \cdot ( t + 3 ) - 1 \cdot t}{( t + 3 ) ^{2}}

Simplify

150 \cdot \frac{1 \cdot ( t + 3 ) - 1 \cdot t}{( t + 3 ) ^{2}} : \frac{450}{( t + 3 ) ^{2}}

= \frac{450}{( t + 3 ) ^{2}}

\int t 9 t^{2} + 4 d t

x^{2}, x^{4} - 3 x^{2}, - 2, 2

x \to a lim (x^{s i n (x)})

\frac{x ^{2}}{2 x + 4}

\frac{d x}{d t} - 2 x = x^{3}

What is the derivative of (150t)/(t+3) ?
The derivative of (150t)/(t+3) is (450)/((t+3)^2)
What is the first derivative of (150t)/(t+3) ?
The first derivative of (150t)/(t+3) is (450)/((t+3)^2)