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

The derivative of ((x-3^3)/((x^3-1)^2)) is (3(x-3)^2(-x^3+6x^2-1))/((x^3-1)^3)

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

The first derivative of ((x-3^3)/((x^3-1)^2)) is (3(x-3)^2(-x^3+6x^2-1))/((x^3-1)^3)

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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

\int_{- 1}^{3} e^{2 x} d x

\int \frac{1}{49 x ^{2} - 64} d x

\frac{d}{d x} (- b sin (x))

\frac{d}{d t} (\frac{t}{( t - 1 ) ^{2}})

What is the derivative of ((x-3^3)/((x^3-1)^2)) ?
The derivative of ((x-3^3)/((x^3-1)^2)) is (3(x-3)^2(-x^3+6x^2-1))/((x^3-1)^3)
What is the first derivative of ((x-3^3)/((x^3-1)^2)) ?
The first derivative of ((x-3^3)/((x^3-1)^2)) is (3(x-3)^2(-x^3+6x^2-1))/((x^3-1)^3)