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

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

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

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

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derivative of

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

= 2 \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

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

Simplify

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

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

\frac{d}{d x} (4 x^{2} e^{- 0.25 x})

(x^{2} + e^{x}) (x)

\int \frac{x ^{2} + 60 x + 60}{x ^{3} - 4 x} d x

n = 1 \sum \infty (- 0.3)^{n - 1}

x \to 3 + lim (\frac{5 x}{x ^{2} - 9})

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