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

The derivative of f(x)=(3x+1)/(5+x) is (14)/((5+x)^2)

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

The first derivative of f(x)=(3x+1)/(5+x) is (14)/((5+x)^2)

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derivative of

f (x) = \frac{3 x + 1}{5 + x}

\frac{14}{( 5 + x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{3 x + 1}{5 + x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 3 x + 1 ) ( 5 + x ) - \frac{d}{d x} ( 5 + x ) ( 3 x + 1 )}{( 5 + x ) ^{2}}

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

\frac{d}{d x} (5 + x) = 1

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

Simplify

\frac{3 ( 5 + x ) - 1 \cdot ( 3 x + 1 )}{( 5 + x ) ^{2}} : \frac{14}{( 5 + x ) ^{2}}

= \frac{14}{( 5 + x ) ^{2}}

\int \frac{7}{x ( x ^{2} + 4 ) ^{2}} d x

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

\frac{d}{d x} (14 (2 x + 5)^{6})

x \to 2 - lim (\frac{4 x}{x - 2})

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

What is the derivative of f(x)=(3x+1)/(5+x) ?
The derivative of f(x)=(3x+1)/(5+x) is (14)/((5+x)^2)
What is the first derivative of f(x)=(3x+1)/(5+x) ?
The first derivative of f(x)=(3x+1)/(5+x) is (14)/((5+x)^2)