What is the derivative of f(x)=(1+2x)/(3+x) ?

The derivative of f(x)=(1+2x)/(3+x) is 5/((3+x)^2)

What is the first derivative of f(x)=(1+2x)/(3+x) ?

The first derivative of f(x)=(1+2x)/(3+x) is 5/((3+x)^2)

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derivative of

f (x) = \frac{1 + 2 x}{3 + x}

\frac{5}{( 3 + x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1 + 2 x}{3 + x})

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{2 ( 3 + x ) - 1 \cdot ( 1 + 2 x )}{( 3 + x ) ^{2}} : \frac{5}{( 3 + x ) ^{2}}

= \frac{5}{( 3 + x ) ^{2}}

f (x) = (x - 1) e^{x^{2} - 4}

\frac{d y}{d x}, x y - 4 x = 5

\int - cos (2 x) d x

\frac{x ^{2}}{2 - x ^{2}}

\int_{1}^{9} \frac{x - 2}{x} d x

What is the derivative of f(x)=(1+2x)/(3+x) ?
The derivative of f(x)=(1+2x)/(3+x) is 5/((3+x)^2)
What is the first derivative of f(x)=(1+2x)/(3+x) ?
The first derivative of f(x)=(1+2x)/(3+x) is 5/((3+x)^2)