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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

x \to 3 lim (x - 10)

x \to - a lim (f (x))

\frac{d y}{d x} + \frac{3 y}{x} = - \frac{1}{x}

\int cos^{4} (x) sin (d) x d x

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