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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

1 \cdot (x + 3) - 1 \cdot x = 3

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

\frac{\partial}{\partial x} (e^{ik x})

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

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

\int x \cdot x^{2} + 5 d x

ln (4 - x)

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