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

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

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

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

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derivative of

\frac{1 - 3 x + x ^{3}}{x ^{3}}

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= \frac{3 ( 2 x - 1 )}{x ^{4}}

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