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

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

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

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

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derivative of

\frac{2 x ^{2} - 3 x + 1}{x}

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (2 x^{2} - 3 x + 1) = 4 x - 3

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

= \frac{( 4 x - 3 ) x - 1 \cdot ( 2 x ^{2} - 3 x + 1 )}{x ^{2}}

Simplify

\frac{( 4 x - 3 ) x - 1 \cdot ( 2 x ^{2} - 3 x + 1 )}{x ^{2}} : \frac{2 x ^{2} - 1}{x ^{2}}

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

p

\frac{\partial}{\partial x} (2 x y + y^{2})

(- 4.5) (1.1)

1 - sec (x)

\int 6 x + 4 d x

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