What is the derivative of ((t^3)/(t^8+5))^2 ?

The derivative of ((t^3)/(t^8+5))^2 is (2t^3(-5t^{10}+15t^2))/((t^8+5)^3)

What is the first derivative of ((t^3)/(t^8+5))^2 ?

The first derivative of ((t^3)/(t^8+5))^2 is (2t^3(-5t^{10}+15t^2))/((t^8+5)^3)

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derivative of

(\frac{t ^{3}}{t ^{8} + 5})^{2}

\frac{2 t ^{3} ( - 5 t ^{10} + 15 t ^{2} )}{( t ^{8} + 5 ) ^{3}}

Solution steps

\frac{d}{d t} ((\frac{t ^{3}}{t ^{8} + 5})^{2})

Apply the chain rule:

2 \cdot \frac{t ^{3}}{t ^{8} + 5} \frac{d}{d t} (\frac{t ^{3}}{t ^{8} + 5})

= 2 \cdot \frac{t ^{3}}{t ^{8} + 5} \frac{d}{d t} (\frac{t ^{3}}{t ^{8} + 5})

\frac{d}{d t} (\frac{t ^{3}}{t ^{8} + 5}) = \frac{- 5 t ^{10} + 15 t ^{2}}{( t ^{8} + 5 ) ^{2}}

= 2 \cdot \frac{t ^{3}}{t ^{8} + 5} \cdot \frac{- 5 t ^{10} + 15 t ^{2}}{( t ^{8} + 5 ) ^{2}}

Simplify

2 \cdot \frac{t ^{3}}{t ^{8} + 5} \cdot \frac{- 5 t ^{10} + 15 t ^{2}}{( t ^{8} + 5 ) ^{2}} : \frac{2 t ^{3} ( - 5 t ^{10} + 15 t ^{2} )}{( t ^{8} + 5 ) ^{3}}

= \frac{2 t ^{3} ( - 5 t ^{10} + 15 t ^{2} )}{( t ^{8} + 5 ) ^{3}}

y = x (x - 2)

1 - 4 x + f (x)

y = (arctan (x))^{2}

\frac{d}{d x} (x^{2} - 16)

\int_{- l n (4)}^{0} 63 e^{t} d t

What is the derivative of ((t^3)/(t^8+5))^2 ?
The derivative of ((t^3)/(t^8+5))^2 is (2t^3(-5t^{10}+15t^2))/((t^8+5)^3)
What is the first derivative of ((t^3)/(t^8+5))^2 ?
The first derivative of ((t^3)/(t^8+5))^2 is (2t^3(-5t^{10}+15t^2))/((t^8+5)^3)