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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{d}{d x} ((2 x^{4} - x + 1) (- x^{5} + 7))

\int_{0}^{x} t^{2} d t

h (x) = (- 2 x - 3)^{5} (3 x + 1)^{3}

f (x) = x^{4}, at x = 2

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