What is the derivative of (4x)/(x+3) ?

The derivative of (4x)/(x+3) is (12)/((x+3)^2)

What is the first derivative of (4x)/(x+3) ?

The first derivative of (4x)/(x+3) is (12)/((x+3)^2)

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derivative of

\frac{4 x}{x + 3}

\frac{12}{( x + 3 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4 x}{x + 3})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} (\frac{x}{x + 3})

Apply the Quotient Rule:

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

= 4 \cdot \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

= 4 \cdot \frac{1 \cdot ( x + 3 ) - 1 \cdot x}{( x + 3 ) ^{2}}

Simplify

4 \cdot \frac{1 \cdot ( x + 3 ) - 1 \cdot x}{( x + 3 ) ^{2}} : \frac{12}{( x + 3 ) ^{2}}

= \frac{12}{( x + 3 ) ^{2}}

x \to - 1 lim (ln (5 + 2 x))

x \to 0 lim (e^{\frac{5}{x}})

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

\int arccos (8 x) d x

\frac{d}{d x} (12 x^{3} - 6 x^{2})

What is the derivative of (4x)/(x+3) ?
The derivative of (4x)/(x+3) is (12)/((x+3)^2)
What is the first derivative of (4x)/(x+3) ?
The first derivative of (4x)/(x+3) is (12)/((x+3)^2)