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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (3 x^{2} - x + 1) = 6 x - 1

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

= \frac{( 6 x - 1 ) x - 1 \cdot ( 3 x ^{2} - x + 1 )}{x ^{2}}

Simplify

\frac{( 6 x - 1 ) x - 1 \cdot ( 3 x ^{2} - x + 1 )}{x ^{2}} : \frac{3 x ^{2} - 1}{x ^{2}}

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

(e^{2 x} - x^{2} - 1)^{^{'}}

\int_{- 1}^{2} x^{2} + 1 d x

\int u 1 - u^{2} d u

\int x \cdot e^{- 2 x} d x

\frac{d}{d x} (\frac{1}{10 x})

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