What is the derivative of ((t^3)/(t^6+7))^2 ?

The derivative of ((t^3)/(t^6+7))^2 is (2t^3(-3t^8+21t^2))/((t^6+7)^3)

What is the first derivative of ((t^3)/(t^6+7))^2 ?

The first derivative of ((t^3)/(t^6+7))^2 is (2t^3(-3t^8+21t^2))/((t^6+7)^3)

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derivative of

(\frac{t ^{3}}{t ^{6} + 7})^{2}

\frac{2 t ^{3} ( - 3 t ^{8} + 21 t ^{2} )}{( t ^{6} + 7 ) ^{3}}

Solution steps

\frac{d}{d t} ((\frac{t ^{3}}{t ^{6} + 7})^{2})

Apply the chain rule:

2 \cdot \frac{t ^{3}}{t ^{6} + 7} \frac{d}{d t} (\frac{t ^{3}}{t ^{6} + 7})

= 2 \cdot \frac{t ^{3}}{t ^{6} + 7} \frac{d}{d t} (\frac{t ^{3}}{t ^{6} + 7})

\frac{d}{d t} (\frac{t ^{3}}{t ^{6} + 7}) = \frac{- 3 t ^{8} + 21 t ^{2}}{( t ^{6} + 7 ) ^{2}}

= 2 \cdot \frac{t ^{3}}{t ^{6} + 7} \cdot \frac{- 3 t ^{8} + 21 t ^{2}}{( t ^{6} + 7 ) ^{2}}

Simplify

2 \cdot \frac{t ^{3}}{t ^{6} + 7} \cdot \frac{- 3 t ^{8} + 21 t ^{2}}{( t ^{6} + 7 ) ^{2}} : \frac{2 t ^{3} ( - 3 t ^{8} + 21 t ^{2} )}{( t ^{6} + 7 ) ^{3}}

= \frac{2 t ^{3} ( - 3 t ^{8} + 21 t ^{2} )}{( t ^{6} + 7 ) ^{3}}

\int \frac{x}{16 + x ^{2}} d x

x \to 3 lim (2 x + ∣ x - 3 ∣)

x \to 7 lim (\frac{x + 5}{x + 9})

x^{2} y^{^{''}} + x y^{^{'}} + 9 y = 10 x

y = x^{3} + 2

What is the derivative of ((t^3)/(t^6+7))^2 ?
The derivative of ((t^3)/(t^6+7))^2 is (2t^3(-3t^8+21t^2))/((t^6+7)^3)
What is the first derivative of ((t^3)/(t^6+7))^2 ?
The first derivative of ((t^3)/(t^6+7))^2 is (2t^3(-3t^8+21t^2))/((t^6+7)^3)