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

The derivative of (x^2-6x-1/((x-3)^2)) is (20)/((x-3)^3)

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

The first derivative of (x^2-6x-1/((x-3)^2)) is (20)/((x-3)^3)

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

\frac{20}{( x - 3 ) ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{( 2 x - 6 ) ( x - 3 ) ^{2} - 2 ( x - 3 ) ( x ^{2} - 6 x - 1 )}{( ( x - 3 ) ^{2} ) ^{2}} : \frac{20}{( x - 3 ) ^{3}}

= \frac{20}{( x - 3 ) ^{3}}

y^{^{''}} + 8 y^{^{'}} + 25 y = 0, y (0) = - 3, y^{^{'}} (0) = 1

\int_{- 5}^{3} ∣ x ∣ + 1 d x

n = 2 \sum \infty \frac{3}{6 ^{n}}

x \to 0 lim (e^{x} cos (5 x))

81 y^{^{''}} + 72 y^{^{'}} + 16 y = 0, y (0) = 5, y^{^{'}} (0) = - 1

What is the derivative of (x^2-6x-1/((x-3)^2)) ?
The derivative of (x^2-6x-1/((x-3)^2)) is (20)/((x-3)^3)
What is the first derivative of (x^2-6x-1/((x-3)^2)) ?
The first derivative of (x^2-6x-1/((x-3)^2)) is (20)/((x-3)^3)