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

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

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

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

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derivative of

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

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

Solution steps

\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}}

= \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

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

Simplify

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

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

\frac{\partial}{\partial x} (4 x y + 3 yz + 5 x y - 48)

\frac{d}{d x} (x^{n} ln (\frac{1}{x}))

\frac{- 3}{( s - 2 ) ^{2}}

\frac{d}{d x} (x^{4} - x^{2})

\int tan (5 x) d x

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