What is the derivative of f(x)=(x^2)/(9+2x) ?

The derivative of f(x)=(x^2)/(9+2x) is (18x+2x^2)/((9+2x)^2)

What is the first derivative of f(x)=(x^2)/(9+2x) ?

The first derivative of f(x)=(x^2)/(9+2x) is (18x+2x^2)/((9+2x)^2)

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derivative of

f (x) = \frac{x ^{2}}{9 + 2 x}

\frac{18 x + 2 x ^{2}}{( 9 + 2 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{9 + 2 x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} ) ( 9 + 2 x ) - \frac{d}{d x} ( 9 + 2 x ) x ^{2}}{( 9 + 2 x ) ^{2}}

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

\frac{d}{d x} (9 + 2 x) = 2

= \frac{2 x ( 9 + 2 x ) - 2 x ^{2}}{( 9 + 2 x ) ^{2}}

Expand

2 x (9 + 2 x) - 2 x^{2} : 18 x + 2 x^{2}

= \frac{18 x + 2 x ^{2}}{( 9 + 2 x ) ^{2}}

What is the derivative of f(x)=(x^2)/(9+2x) ?
The derivative of f(x)=(x^2)/(9+2x) is (18x+2x^2)/((9+2x)^2)
What is the first derivative of f(x)=(x^2)/(9+2x) ?
The first derivative of f(x)=(x^2)/(9+2x) is (18x+2x^2)/((9+2x)^2)