What is the derivative of ((t^3)/(t^6+5))^2 ?

The derivative of ((t^3)/(t^6+5))^2 is (2t^3(-3t^8+15t^2))/((t^6+5)^3)

What is the first derivative of ((t^3)/(t^6+5))^2 ?

The first derivative of ((t^3)/(t^6+5))^2 is (2t^3(-3t^8+15t^2))/((t^6+5)^3)

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derivative of

(\frac{t ^{3}}{t ^{6} + 5})^{2}

\frac{2 t ^{3} ( - 3 t ^{8} + 15 t ^{2} )}{( t ^{6} + 5 ) ^{3}}

Solution steps

\frac{d}{d t} ((\frac{t ^{3}}{t ^{6} + 5})^{2})

Apply the chain rule:

2 \cdot \frac{t ^{3}}{t ^{6} + 5} \frac{d}{d t} (\frac{t ^{3}}{t ^{6} + 5})

= 2 \cdot \frac{t ^{3}}{t ^{6} + 5} \frac{d}{d t} (\frac{t ^{3}}{t ^{6} + 5})

\frac{d}{d t} (\frac{t ^{3}}{t ^{6} + 5}) = \frac{- 3 t ^{8} + 15 t ^{2}}{( t ^{6} + 5 ) ^{2}}

= 2 \cdot \frac{t ^{3}}{t ^{6} + 5} \cdot \frac{- 3 t ^{8} + 15 t ^{2}}{( t ^{6} + 5 ) ^{2}}

Simplify

2 \cdot \frac{t ^{3}}{t ^{6} + 5} \cdot \frac{- 3 t ^{8} + 15 t ^{2}}{( t ^{6} + 5 ) ^{2}} : \frac{2 t ^{3} ( - 3 t ^{8} + 15 t ^{2} )}{( t ^{6} + 5 ) ^{3}}

= \frac{2 t ^{3} ( - 3 t ^{8} + 15 t ^{2} )}{( t ^{6} + 5 ) ^{3}}

\frac{d}{d x} (\frac{e ^{2 x}}{1 + sin ( π x )})

x \to 3 - lim (- \frac{1}{x - 3})

\int_{1}^{3} (x^{2} + 1) d x

y^{^{''}} + 3 y^{^{'}} = 6 e^{- 3 t}, y (0) = 8, y^{^{'}} (0) = - 4

\frac{d}{d x} (e^{x} x^{3} + 6 e^{x} x^{2} + 6 e^{x} x)

What is the derivative of ((t^3)/(t^6+5))^2 ?
The derivative of ((t^3)/(t^6+5))^2 is (2t^3(-3t^8+15t^2))/((t^6+5)^3)
What is the first derivative of ((t^3)/(t^6+5))^2 ?
The first derivative of ((t^3)/(t^6+5))^2 is (2t^3(-3t^8+15t^2))/((t^6+5)^3)