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

The derivative of (2x/(x^6+3x^2)) is -(2(5x^4+3))/(x^2(x^4+3)^2)

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

The first derivative of (2x/(x^6+3x^2)) is -(2(5x^4+3))/(x^2(x^4+3)^2)

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

- \frac{2 ( 5 x ^{4} + 3 )}{x ^{2} ( x ^{4} + 3 ) ^{2}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= 2 \cdot \frac{\frac{d x}{d x} ( x ^{6} + 3 x ^{2} ) - \frac{d}{d x} ( x ^{6} + 3 x ^{2} ) x}{( x ^{6} + 3 x ^{2} ) ^{2}}

\frac{d x}{d x} = 1

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

= 2 \cdot \frac{1 \cdot ( x ^{6} + 3 x ^{2} ) - ( 6 x ^{5} + 6 x ) x}{( x ^{6} + 3 x ^{2} ) ^{2}}

Simplify

2 \cdot \frac{1 \cdot ( x ^{6} + 3 x ^{2} ) - ( 6 x ^{5} + 6 x ) x}{( x ^{6} + 3 x ^{2} ) ^{2}} : - \frac{2 ( 5 x ^{4} + 3 )}{x ^{2} ( x ^{4} + 3 ) ^{2}}

= - \frac{2 ( 5 x ^{4} + 3 )}{x ^{2} ( x ^{4} + 3 ) ^{2}}

arccos (3 x)

\int u sin (u) d u

x y + y^{^{'}} = 2 x, y (0) = 5

\frac{d ^{2} y}{d x ^{2}} - 3 \frac{d y}{d x} + 2 y = 4 x^{2}

\int \frac{2 x ^{2}}{x ^{2} + 8} d x

What is the derivative of (2x/(x^6+3x^2)) ?
The derivative of (2x/(x^6+3x^2)) is -(2(5x^4+3))/(x^2(x^4+3)^2)
What is the first derivative of (2x/(x^6+3x^2)) ?
The first derivative of (2x/(x^6+3x^2)) is -(2(5x^4+3))/(x^2(x^4+3)^2)