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

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

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

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

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derivative of

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

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

Solution steps

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

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

\frac{d}{d x} (2 + x) = 1

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

Simplify

\frac{2 x ( 2 + x ) - 1 \cdot x ^{2}}{( 2 + x ) ^{2}} : \frac{4 x + x ^{2}}{( 2 + x ) ^{2}}

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

x^{2} - 2 x, x + 4

y = x^{2} - 1, y = - x^{2} + 1

sin (2 x) d x + cos (3 y) d y = 0

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

\frac{\partial}{\partial x} (\frac{7 x}{y})

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