What is the derivative of (x^2-10x+9/((x-5)^2)) ?

The derivative of (x^2-10x+9/((x-5)^2)) is (32)/((x-5)^3)

What is the first derivative of (x^2-10x+9/((x-5)^2)) ?

The first derivative of (x^2-10x+9/((x-5)^2)) is (32)/((x-5)^3)

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\frac{d}{d x} (\frac{x ^{2} - 10 x + 9}{( x - 5 ) ^{2}})

\frac{32}{( x - 5 ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} - 10 x + 9}{( x - 5 ) ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} - 10 x + 9 ) ( x - 5 ) ^{2} - \frac{d}{d x} ( ( x - 5 ) ^{2} ) ( x ^{2} - 10 x + 9 )}{( ( x - 5 ) ^{2} ) ^{2}}

\frac{d}{d x} (x^{2} - 10 x + 9) = 2 x - 10

\frac{d}{d x} ((x - 5)^{2}) = 2 (x - 5)

= \frac{( 2 x - 10 ) ( x - 5 ) ^{2} - 2 ( x - 5 ) ( x ^{2} - 10 x + 9 )}{( ( x - 5 ) ^{2} ) ^{2}}

Simplify

\frac{( 2 x - 10 ) ( x - 5 ) ^{2} - 2 ( x - 5 ) ( x ^{2} - 10 x + 9 )}{( ( x - 5 ) ^{2} ) ^{2}} : \frac{32}{( x - 5 ) ^{3}}

= \frac{32}{( x - 5 ) ^{3}}

f (x) = \frac{4}{2 - x}

- \frac{36 ( x - 1 )}{( x + 3 ) ^{3}}

2 x^{2} + 5, - 2, 3

\int sin (3 θ) d θ

\frac{( 1 - 4 t )}{( 6 + t )}

What is the derivative of (x^2-10x+9/((x-5)^2)) ?
The derivative of (x^2-10x+9/((x-5)^2)) is (32)/((x-5)^3)
What is the first derivative of (x^2-10x+9/((x-5)^2)) ?
The first derivative of (x^2-10x+9/((x-5)^2)) is (32)/((x-5)^3)