What is the derivative of (3(2x+1)/(sqrt(6x+6x^2))) ?

The derivative of (3(2x+1)/(sqrt(6x+6x^2))) is -3/(2x(x+1)sqrt(6x^2+6x))

What is the first derivative of (3(2x+1)/(sqrt(6x+6x^2))) ?

The first derivative of (3(2x+1)/(sqrt(6x+6x^2))) is -3/(2x(x+1)sqrt(6x^2+6x))

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{d y}{d x} = sin (3 y) ln (x)

sin (x) + \frac{7}{2} cot (x)

\int y e^{- x y} d x

f (x) = \frac{x - 2}{x ^{2}}

\int_{0}^{a} x a^{2} - x^{2} d x

What is the derivative of (3(2x+1)/(sqrt(6x+6x^2))) ?
The derivative of (3(2x+1)/(sqrt(6x+6x^2))) is -3/(2x(x+1)sqrt(6x^2+6x))
What is the first derivative of (3(2x+1)/(sqrt(6x+6x^2))) ?
The first derivative of (3(2x+1)/(sqrt(6x+6x^2))) is -3/(2x(x+1)sqrt(6x^2+6x))