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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

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

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

4 x ln (2 x + 1)

\frac{d}{d q} (2600 - 13 q)

cos (x) + 1

\frac{1}{( a - x )}

(4 - 3 x)^{10}

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