What is the derivative of 6/(2x+1) ?

The derivative of 6/(2x+1) is -(12)/((2x+1)^2)

What is the first derivative of 6/(2x+1) ?

The first derivative of 6/(2x+1) is -(12)/((2x+1)^2)

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\frac{d}{d x} (\frac{6}{2 x + 1})

- \frac{12}{( 2 x + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{6}{2 x + 1})

Take the constant out:

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

= 6 \frac{d}{d x} (\frac{1}{2 x + 1})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= 6 \frac{d}{d x} ((2 x + 1)^{- 1})

Apply the chain rule:

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

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

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

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

Simplify

6 (- \frac{1}{( 2 x + 1 ) ^{2}} \cdot 2) : - \frac{12}{( 2 x + 1 ) ^{2}}

= - \frac{12}{( 2 x + 1 ) ^{2}}

\frac{d}{d x} (\frac{x + 1}{x + 6})^{8}

y^{^{'}} = \frac{1}{( t - 1 ) ( y + 1 )}

f (x) = x^{3} (x - 6)^{2}

f (x) = x - 1 + x + 1

y = (\frac{( x + 2 )}{( x - 2 )})^{2}, at x = 3

What is the derivative of 6/(2x+1) ?
The derivative of 6/(2x+1) is -(12)/((2x+1)^2)
What is the first derivative of 6/(2x+1) ?
The first derivative of 6/(2x+1) is -(12)/((2x+1)^2)