What is the derivative of f(x)=((x^3)/(x^8+5))^2 ?

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

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

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

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derivative of

f (x) = (\frac{x ^{3}}{x ^{8} + 5})^{2}

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d y}{d x} = x^{\frac{1}{4}} + x^{- \frac{3}{5}}

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