What is the derivative of ((-5x+1^3)/((3x-3)^6)) ?

The derivative of ((-5x+1^3)/((3x-3)^6)) is -((-5x+1)^2(-5x-3))/(243(x-1)^7)

What is the first derivative of ((-5x+1^3)/((3x-3)^6)) ?

The first derivative of ((-5x+1^3)/((3x-3)^6)) is -((-5x+1)^2(-5x-3))/(243(x-1)^7)

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\frac{d}{d x} (\frac{( - 5 x + 1 ) ^{3}}{( 3 x - 3 ) ^{6}})

- \frac{( - 5 x + 1 ) ^{2} ( - 5 x - 3 )}{243 ( x - 1 ) ^{7}}

Solution steps

\frac{d}{d x} (\frac{( - 5 x + 1 ) ^{3}}{( 3 x - 3 ) ^{6}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( ( - 5 x + 1 ) ^{3} ) ( 3 x - 3 ) ^{6} - \frac{d}{d x} ( ( 3 x - 3 ) ^{6} ) ( - 5 x + 1 ) ^{3}}{( ( 3 x - 3 ) ^{6} ) ^{2}}

\frac{d}{d x} ((- 5 x + 1)^{3}) = - 15 (- 5 x + 1)^{2}

\frac{d}{d x} ((3 x - 3)^{6}) = 18 (3 x - 3)^{5}

= \frac{( - 15 ( - 5 x + 1 ) ^{2} ) ( 3 x - 3 ) ^{6} - 18 ( 3 x - 3 ) ^{5} ( - 5 x + 1 ) ^{3}}{( ( 3 x - 3 ) ^{6} ) ^{2}}

Simplify

\frac{( - 15 ( - 5 x + 1 ) ^{2} ) ( 3 x - 3 ) ^{6} - 18 ( 3 x - 3 ) ^{5} ( - 5 x + 1 ) ^{3}}{( ( 3 x - 3 ) ^{6} ) ^{2}} : - \frac{( - 5 x + 1 ) ^{2} ( - 5 x - 3 )}{243 ( x - 1 ) ^{7}}

= - \frac{( - 5 x + 1 ) ^{2} ( - 5 x - 3 )}{243 ( x - 1 ) ^{7}}

\frac{\partial}{\partial x} (x^{2} - y^{2} - 2 z^{2})

\frac{d}{d x} (\frac{12 x ^{5} + 8 x ^{3} - 2 x ^{2}}{4 x ^{2}})

\frac{8}{e ^{x} + e ^{- x}}

e^{- 6 x}, 0

\int x ln (5 x) d x

What is the derivative of ((-5x+1^3)/((3x-3)^6)) ?
The derivative of ((-5x+1^3)/((3x-3)^6)) is -((-5x+1)^2(-5x-3))/(243(x-1)^7)
What is the first derivative of ((-5x+1^3)/((3x-3)^6)) ?
The first derivative of ((-5x+1^3)/((3x-3)^6)) is -((-5x+1)^2(-5x-3))/(243(x-1)^7)