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

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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

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

\int \frac{1}{h x + a} d x

\frac{d y}{d x} = csc (x) - y cot (x)

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

\int \frac{sin ( x )}{2 - cos ( x )} d x

y = 2 x^{2}, y = 3 - x, 0, 3

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