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

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

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

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

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derivative of

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

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

Solution steps

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

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

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

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

Simplify

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

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

\frac{d y}{d x} + y cos (x) = 5 cos (x), y (0) = 7

\frac{d}{d x} (x^{7})

\frac{\partial}{\partial x} (9 e^{y} (y^{2} - x^{2}))

\int t ln (t + 4) d t

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