What is the derivative of ((t^3)/(t^8+7))^2 ?

The derivative of ((t^3)/(t^8+7))^2 is (2t^3(-5t^{10}+21t^2))/((t^8+7)^3)

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

The first derivative of ((t^3)/(t^8+7))^2 is (2t^3(-5t^{10}+21t^2))/((t^8+7)^3)

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derivative of

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

\frac{2 t ^{3} ( - 5 t ^{10} + 21 t ^{2} )}{( t ^{8} + 7 ) ^{3}}

Solution steps

\frac{d}{d t} ((\frac{t ^{3}}{t ^{8} + 7})^{2})

Apply the chain rule:

2 \cdot \frac{t ^{3}}{t ^{8} + 7} \frac{d}{d t} (\frac{t ^{3}}{t ^{8} + 7})

= 2 \cdot \frac{t ^{3}}{t ^{8} + 7} \frac{d}{d t} (\frac{t ^{3}}{t ^{8} + 7})

\frac{d}{d t} (\frac{t ^{3}}{t ^{8} + 7}) = \frac{- 5 t ^{10} + 21 t ^{2}}{( t ^{8} + 7 ) ^{2}}

= 2 \cdot \frac{t ^{3}}{t ^{8} + 7} \cdot \frac{- 5 t ^{10} + 21 t ^{2}}{( t ^{8} + 7 ) ^{2}}

Simplify

2 \cdot \frac{t ^{3}}{t ^{8} + 7} \cdot \frac{- 5 t ^{10} + 21 t ^{2}}{( t ^{8} + 7 ) ^{2}} : \frac{2 t ^{3} ( - 5 t ^{10} + 21 t ^{2} )}{( t ^{8} + 7 ) ^{3}}

= \frac{2 t ^{3} ( - 5 t ^{10} + 21 t ^{2} )}{( t ^{8} + 7 ) ^{3}}

\int (x + 1) ln (2 x + 4) d x

\frac{d}{d x} ((\frac{1}{x ^{2}} - \frac{3}{x ^{4}}) (x + 7 x^{3}))

\frac{d y}{d x} = x (9 - y)

\frac{d}{d x} (\frac{1 + 3 x}{1 - 3 x})

x \to \infty lim (9)

What is the derivative of ((t^3)/(t^8+7))^2 ?
The derivative of ((t^3)/(t^8+7))^2 is (2t^3(-5t^{10}+21t^2))/((t^8+7)^3)
What is the first derivative of ((t^3)/(t^8+7))^2 ?
The first derivative of ((t^3)/(t^8+7))^2 is (2t^3(-5t^{10}+21t^2))/((t^8+7)^3)