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

The derivative of f(x)=(2x^2)/(x+3) is (2(x^2+6x))/((x+3)^2)

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

The first derivative of f(x)=(2x^2)/(x+3) is (2(x^2+6x))/((x+3)^2)

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derivative of

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

(2 x - 1)^{2}

x \to 0 - lim (18 - x^{2})

\frac{d}{d x} (\frac{1}{x + c})

\int (2 x + 1)^{9} d x

\frac{d}{d t} (t^{2} + 2)

What is the derivative of f(x)=(2x^2)/(x+3) ?
The derivative of f(x)=(2x^2)/(x+3) is (2(x^2+6x))/((x+3)^2)
What is the first derivative of f(x)=(2x^2)/(x+3) ?
The first derivative of f(x)=(2x^2)/(x+3) is (2(x^2+6x))/((x+3)^2)