What is the derivative of ((1-2x)^3)/(x^3) ?

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

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

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

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derivative of

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

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

Solution steps

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

\frac{d}{d x} ((1 - 2 x)^{3}) = - 6 (1 - 2 x)^{2}

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

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

Simplify

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

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

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

f (x) = x^{l n (x)}

\int 12 x^{2} - 7 x + 5 d x

\int \frac{t}{t ^{4} + 81} d t

f (x) = \frac{1}{1 + x}

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