What is the derivative of x/((1-x^3)) ?

The derivative of x/((1-x^3)) is (1+2x)/((1-x)^4)

What is the first derivative of x/((1-x^3)) ?

The first derivative of x/((1-x^3)) is (1+2x)/((1-x)^4)

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\frac{d}{d x} (\frac{x}{( 1 - x ) ^{3}})

\frac{1 + 2 x}{( 1 - x ) ^{4}}

Solution steps

\frac{d}{d x} (\frac{x}{( 1 - x ) ^{3}})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( 1 - x ) ^{3} - \frac{d}{d x} ( ( 1 - x ) ^{3} ) x}{( ( 1 - x ) ^{3} ) ^{2}}

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

\frac{d}{d x} ((1 - x)^{3}) = - 3 (1 - x)^{2}

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

Simplify

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

= \frac{1 + 2 x}{( 1 - x ) ^{4}}

y^{^{''}} - 2 y^{^{'}} + y = \frac{e ^{t}}{( 1 + t ^{2} )}

\int \frac{1}{x} e^{- x} d x

n = 0 \sum \infty cos (5 nπ)

f (x) = ln^{5} (x)

y^{^{'}} - 4 y = 10 sin (2 t)

What is the derivative of x/((1-x^3)) ?
The derivative of x/((1-x^3)) is (1+2x)/((1-x)^4)
What is the first derivative of x/((1-x^3)) ?
The first derivative of x/((1-x^3)) is (1+2x)/((1-x)^4)