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

The derivative of ((x^3)/(x^8+3))^2 is (2x^3(-5x^{10}+9x^2))/((x^8+3)^3)

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

The first derivative of ((x^3)/(x^8+3))^2 is (2x^3(-5x^{10}+9x^2))/((x^8+3)^3)

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derivative of

(\frac{x ^{3}}{x ^{8} + 3})^{2}

\frac{2 x ^{3} ( - 5 x ^{10} + 9 x ^{2} )}{( x ^{8} + 3 ) ^{3}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x ^{3}}{x ^{8} + 3}) = \frac{- 5 x ^{10} + 9 x ^{2}}{( x ^{8} + 3 ) ^{2}}

= 2 \cdot \frac{x ^{3}}{x ^{8} + 3} \cdot \frac{- 5 x ^{10} + 9 x ^{2}}{( x ^{8} + 3 ) ^{2}}

Simplify

2 \cdot \frac{x ^{3}}{x ^{8} + 3} \cdot \frac{- 5 x ^{10} + 9 x ^{2}}{( x ^{8} + 3 ) ^{2}} : \frac{2 x ^{3} ( - 5 x ^{10} + 9 x ^{2} )}{( x ^{8} + 3 ) ^{3}}

= \frac{2 x ^{3} ( - 5 x ^{10} + 9 x ^{2} )}{( x ^{8} + 3 ) ^{3}}

f (x) = ((2 x - 2) (3 x^{3} - x^{2} + 1))

\int_{2}^{5} ∣ x - 3 ∣ d x

(x^{2} + 1) y^{^{'}} + 8 x (y - 1) = 0

x^{4} - 8 x^{3}

\frac{\partial}{\partial x} (\frac{3}{3 x + 2 y})

What is the derivative of ((x^3)/(x^8+3))^2 ?
The derivative of ((x^3)/(x^8+3))^2 is (2x^3(-5x^{10}+9x^2))/((x^8+3)^3)
What is the first derivative of ((x^3)/(x^8+3))^2 ?
The first derivative of ((x^3)/(x^8+3))^2 is (2x^3(-5x^{10}+9x^2))/((x^8+3)^3)