What is the derivative of (4x/(3x+1)) ?

The derivative of (4x/(3x+1)) is 4/((3x+1)^2)

What is the first derivative of (4x/(3x+1)) ?

The first derivative of (4x/(3x+1)) is 4/((3x+1)^2)

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\frac{d}{d x} (\frac{4 x}{3 x + 1})

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

Solution steps

\frac{d}{d x} (\frac{4 x}{3 x + 1})

Take the constant out:

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

= 4 \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}}

= 4 \cdot \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

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

Simplify

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

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

x \to 5 lim ((3 + \frac{1}{x})^{3})

y^{^{'}} = \frac{4 x}{e ^{x}}

x^{2} (1 - 9 x)

f (x) = x^{4} - 20 x^{2} + 64

\frac{d}{d x} (ln (\frac{sin ( x )}{cos ( x )}))

What is the derivative of (4x/(3x+1)) ?
The derivative of (4x/(3x+1)) is 4/((3x+1)^2)
What is the first derivative of (4x/(3x+1)) ?
The first derivative of (4x/(3x+1)) is 4/((3x+1)^2)