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

The derivative of (2+x^3/(2-x^3)) is (12x^2)/((2-x^3)^2)

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

The first derivative of (2+x^3/(2-x^3)) is (12x^2)/((2-x^3)^2)

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

\frac{12 x ^{2}}{( 2 - x ^{3} ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{3 x ^{2} ( 2 - x ^{3} ) - ( - 3 x ^{2} ) ( 2 + x ^{3} )}{( 2 - x ^{3} ) ^{2}} : \frac{12 x ^{2}}{( 2 - x ^{3} ) ^{2}}

= \frac{12 x ^{2}}{( 2 - x ^{3} ) ^{2}}

f (x) = tan (x) - sin (x)

\int 2 x ln (6 x) d x

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What is the derivative of (2+x^3/(2-x^3)) ?
The derivative of (2+x^3/(2-x^3)) is (12x^2)/((2-x^3)^2)
What is the first derivative of (2+x^3/(2-x^3)) ?
The first derivative of (2+x^3/(2-x^3)) is (12x^2)/((2-x^3)^2)