What is the derivative of (4x^2-5x+1)/x ?

The derivative of (4x^2-5x+1)/x is (4x^2-1)/(x^2)

What is the first derivative of (4x^2-5x+1)/x ?

The first derivative of (4x^2-5x+1)/x is (4x^2-1)/(x^2)

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derivative of

\frac{4 x ^{2} - 5 x + 1}{x}

\frac{4 x ^{2} - 1}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{4 x ^{2} - 5 x + 1}{x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 4 x ^{2} - 5 x + 1 ) x - \frac{d x}{d x} ( 4 x ^{2} - 5 x + 1 )}{x ^{2}}

\frac{d}{d x} (4 x^{2} - 5 x + 1) = 8 x - 5

\frac{d x}{d x} = 1

= \frac{( 8 x - 5 ) x - 1 \cdot ( 4 x ^{2} - 5 x + 1 )}{x ^{2}}

Simplify

\frac{( 8 x - 5 ) x - 1 \cdot ( 4 x ^{2} - 5 x + 1 )}{x ^{2}} : \frac{4 x ^{2} - 1}{x ^{2}}

= \frac{4 x ^{2} - 1}{x ^{2}}

What is the derivative of (4x^2-5x+1)/x ?
The derivative of (4x^2-5x+1)/x is (4x^2-1)/(x^2)
What is the first derivative of (4x^2-5x+1)/x ?
The first derivative of (4x^2-5x+1)/x is (4x^2-1)/(x^2)