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

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

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

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

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derivative of

\frac{x ^{2} - 4 x + 3}{x ^{2}}

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

7 y^{^{''}} + 7 y^{^{'}} - 14 y = 0

7 (3 x^{2} ln (5 x) + x^{2})

x \to 2 + lim (8 - x^{3})

\frac{d}{d t} (3 t cos (t))

10 sin (x)

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