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

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

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

expand

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

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

Solution steps

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

Expand

(3 x - 1) x^{2} : 3 x^{3} - x^{2}

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

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

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

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

Apply rule

\frac{a}{a} = 1

\frac{x}{x} = 1

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

\frac{1 - t ^{2}}{( 1 + t ^{2} ) ^{2}}

(6 x + 9 y + 11) d x + (9 x - 4 y + 3) d y

\frac{( x - 1 ) ( x - 3 ) ( x - 6 )}{6}

cos (x) (cos (x) + (- s) in x)

\frac{( 8 y + x ^{3} ) ^{2}}{4}

What is expand derivative of (3x-1x^2)+(x-1)/x ?
The solution to expand derivative of (3x-1x^2)+(x-1)/x is derivative of 3x^3-x^2+1-1/x