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

The derivative of (3x+6/(2sqrt(x+3))) is (3x+12)/(4(x+3)sqrt(x+3))

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

The first derivative of (3x+6/(2sqrt(x+3))) is (3x+12)/(4(x+3)sqrt(x+3))

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

\frac{3 x + 12}{4 ( x + 3 ) x + 3}

Solution steps

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

Take the constant out:

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

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

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

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

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

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

Simplify

\frac{1}{2} \cdot \frac{3 x + 3 - \frac{1}{2 x + 3} ( 3 x + 6 )}{( x + 3 ) ^{2}} : \frac{3 x + 12}{4 ( x + 3 ) x + 3}

= \frac{3 x + 12}{4 ( x + 3 ) x + 3}

What is the derivative of (3x+6/(2sqrt(x+3))) ?
The derivative of (3x+6/(2sqrt(x+3))) is (3x+12)/(4(x+3)sqrt(x+3))
What is the first derivative of (3x+6/(2sqrt(x+3))) ?
The first derivative of (3x+6/(2sqrt(x+3))) is (3x+12)/(4(x+3)sqrt(x+3))