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

The derivative of (3x^2+3x-2)/(2xsqrt(x)) is (3(x^2-x+2))/(4x^{5/2)}

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

The first derivative of (3x^2+3x-2)/(2xsqrt(x)) is (3(x^2-x+2))/(4x^{5/2)}

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derivative of

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

\frac{3 ( x ^{2} - x + 2 )}{4 x ^{\frac{5}{2}}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x x) = \frac{3 x}{2}

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

Simplify

\frac{1}{2} \cdot \frac{( 6 x + 3 ) x x - \frac{3 x}{2} ( 3 x ^{2} + 3 x - 2 )}{( x x ) ^{2}} : \frac{3 ( x ^{2} - x + 2 )}{4 x ^{\frac{5}{2}}}

= \frac{3 ( x ^{2} - x + 2 )}{4 x ^{\frac{5}{2}}}

(5.5) (2.3)

\int t^{2} e^{- 5 t} d t

x^{2} y^{^{''}} - 9 x y^{^{'}} + 25 y = 0

f (x) = 36 x^{- 2} - 2 x^{- 4} + 2

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

What is the derivative of (3x^2+3x-2)/(2xsqrt(x)) ?
The derivative of (3x^2+3x-2)/(2xsqrt(x)) is (3(x^2-x+2))/(4x^{5/2)}
What is the first derivative of (3x^2+3x-2)/(2xsqrt(x)) ?
The first derivative of (3x^2+3x-2)/(2xsqrt(x)) is (3(x^2-x+2))/(4x^{5/2)}