What is the derivative of y=(3x^2)/(2x+4) ?

The derivative of y=(3x^2)/(2x+4) is (3x(x+4))/(2(x+2)^2)

What is the first derivative of y=(3x^2)/(2x+4) ?

The first derivative of y=(3x^2)/(2x+4) is (3x(x+4))/(2(x+2)^2)

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derivative of

y = \frac{3 x ^{2}}{2 x + 4}

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int 2 x sin^{2} (x) d x

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What is the derivative of y=(3x^2)/(2x+4) ?
The derivative of y=(3x^2)/(2x+4) is (3x(x+4))/(2(x+2)^2)
What is the first derivative of y=(3x^2)/(2x+4) ?
The first derivative of y=(3x^2)/(2x+4) is (3x(x+4))/(2(x+2)^2)