What is the derivative of ((x^3/(x^8+9))^2) ?

The derivative of ((x^3/(x^8+9))^2) is (2x^3(-5x^{10}+27x^2))/((x^8+9)^3)

What is the first derivative of ((x^3/(x^8+9))^2) ?

The first derivative of ((x^3/(x^8+9))^2) is (2x^3(-5x^{10}+27x^2))/((x^8+9)^3)

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\frac{d}{d x} ((\frac{x ^{3}}{x ^{8} + 9})^{2})

\frac{2 x ^{3} ( - 5 x ^{10} + 27 x ^{2} )}{( x ^{8} + 9 ) ^{3}}

Solution steps

\frac{d}{d x} ((\frac{x ^{3}}{x ^{8} + 9})^{2})

Apply the chain rule:

2 \cdot \frac{x ^{3}}{x ^{8} + 9} \frac{d}{d x} (\frac{x ^{3}}{x ^{8} + 9})

= 2 \cdot \frac{x ^{3}}{x ^{8} + 9} \frac{d}{d x} (\frac{x ^{3}}{x ^{8} + 9})

\frac{d}{d x} (\frac{x ^{3}}{x ^{8} + 9}) = \frac{- 5 x ^{10} + 27 x ^{2}}{( x ^{8} + 9 ) ^{2}}

= 2 \cdot \frac{x ^{3}}{x ^{8} + 9} \cdot \frac{- 5 x ^{10} + 27 x ^{2}}{( x ^{8} + 9 ) ^{2}}

Simplify

2 \cdot \frac{x ^{3}}{x ^{8} + 9} \cdot \frac{- 5 x ^{10} + 27 x ^{2}}{( x ^{8} + 9 ) ^{2}} : \frac{2 x ^{3} ( - 5 x ^{10} + 27 x ^{2} )}{( x ^{8} + 9 ) ^{3}}

= \frac{2 x ^{3} ( - 5 x ^{10} + 27 x ^{2} )}{( x ^{8} + 9 ) ^{3}}

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

\frac{d}{d x} (\frac{x ^{2}}{4})

\frac{sin ( x )}{x}

\int \frac{12}{x ^{4}} d x

arctan (\frac{x}{2})

What is the derivative of ((x^3/(x^8+9))^2) ?
The derivative of ((x^3/(x^8+9))^2) is (2x^3(-5x^{10}+27x^2))/((x^8+9)^3)
What is the first derivative of ((x^3/(x^8+9))^2) ?
The first derivative of ((x^3/(x^8+9))^2) is (2x^3(-5x^{10}+27x^2))/((x^8+9)^3)