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

The derivative of ((t^2)/((t^3+2)))^2 is (2t^2(-t^4+4t))/((t^3+2)^3)

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

The first derivative of ((t^2)/((t^3+2)))^2 is (2t^2(-t^4+4t))/((t^3+2)^3)

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derivative of

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

\frac{2 t ^{2} ( - t ^{4} + 4 t )}{( t ^{3} + 2 ) ^{3}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d t} (\frac{t ^{2}}{t ^{3} + 2}) = \frac{- t ^{4} + 4 t}{( t ^{3} + 2 ) ^{2}}

= 2 \cdot \frac{t ^{2}}{t ^{3} + 2} \cdot \frac{- t ^{4} + 4 t}{( t ^{3} + 2 ) ^{2}}

Simplify

2 \cdot \frac{t ^{2}}{t ^{3} + 2} \cdot \frac{- t ^{4} + 4 t}{( t ^{3} + 2 ) ^{2}} : \frac{2 t ^{2} ( - t ^{4} + 4 t )}{( t ^{3} + 2 ) ^{3}}

= \frac{2 t ^{2} ( - t ^{4} + 4 t )}{( t ^{3} + 2 ) ^{3}}

What is the derivative of ((t^2)/((t^3+2)))^2 ?
The derivative of ((t^2)/((t^3+2)))^2 is (2t^2(-t^4+4t))/((t^3+2)^3)
What is the first derivative of ((t^2)/((t^3+2)))^2 ?
The first derivative of ((t^2)/((t^3+2)))^2 is (2t^2(-t^4+4t))/((t^3+2)^3)