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

The derivative of ((x-2(x^2-x+1))/(sqrt(x))) is (5x^3-9x^2+3x+2)/(2xsqrt(x))

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

The first derivative of ((x-2(x^2-x+1))/(sqrt(x))) is (5x^3-9x^2+3x+2)/(2xsqrt(x))

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

\frac{5 x ^{3} - 9 x ^{2} + 3 x + 2}{2 x x}

Solution steps

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

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

\frac{d}{d x} (x) = \frac{1}{2 x}

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

Simplify

\frac{( 3 x ^{2} - 6 x + 3 ) x - \frac{1}{2 x} ( x - 2 ) ( x ^{2} - x + 1 )}{( x ) ^{2}} : \frac{5 x ^{3} - 9 x ^{2} + 3 x + 2}{2 x x}

= \frac{5 x ^{3} - 9 x ^{2} + 3 x + 2}{2 x x}

\frac{s ^{3} + 5 s ^{2} + 9 s + 7}{s ^{2} + 3 s + 2}

\frac{\partial}{\partial x} (a x^{2})

x \to - 3 lim (\frac{x ^{2} - 4}{3 - x})

\frac{x - 4}{x + 2}

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

What is the derivative of ((x-2(x^2-x+1))/(sqrt(x))) ?
The derivative of ((x-2(x^2-x+1))/(sqrt(x))) is (5x^3-9x^2+3x+2)/(2xsqrt(x))
What is the first derivative of ((x-2(x^2-x+1))/(sqrt(x))) ?
The first derivative of ((x-2(x^2-x+1))/(sqrt(x))) is (5x^3-9x^2+3x+2)/(2xsqrt(x))