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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\frac{d}{d x} (\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}}

x^{2} + x y + 2 y^{2} = 28, (2, 3)

t^{2} y^{^{''}} + 7 t y^{^{'}} + 10 y = 0

\int tan (4 x) sec^{5} (4 x) d x

x \to 7 - lim (\frac{1}{x - 7})

x^{2} + 6

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)