What is the derivative of ((3t-2)^3)/(t+5) ?

The derivative of ((3t-2)^3)/(t+5) is (9(3t-2)^2(t+5)-(3t-2)^3)/((t+5)^2)

What is the first derivative of ((3t-2)^3)/(t+5) ?

The first derivative of ((3t-2)^3)/(t+5) is (9(3t-2)^2(t+5)-(3t-2)^3)/((t+5)^2)

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derivative of

\frac{( 3 t - 2 ) ^{3}}{t + 5}

\frac{9 ( 3 t - 2 ) ^{2} ( t + 5 ) - ( 3 t - 2 ) ^{3}}{( t + 5 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d t} ((3 t - 2)^{3}) = 9 (3 t - 2)^{2}

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

= \frac{9 ( 3 t - 2 ) ^{2} ( t + 5 ) - 1 \cdot ( 3 t - 2 ) ^{3}}{( t + 5 ) ^{2}}

Simplify

= \frac{9 ( 3 t - 2 ) ^{2} ( t + 5 ) - ( 3 t - 2 ) ^{3}}{( t + 5 ) ^{2}}

What is the derivative of ((3t-2)^3)/(t+5) ?
The derivative of ((3t-2)^3)/(t+5) is (9(3t-2)^2(t+5)-(3t-2)^3)/((t+5)^2)
What is the first derivative of ((3t-2)^3)/(t+5) ?
The first derivative of ((3t-2)^3)/(t+5) is (9(3t-2)^2(t+5)-(3t-2)^3)/((t+5)^2)