What is the derivative of (ln(x+1)/(4x+2)) ?

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

What is the first derivative of (ln(x+1)/(4x+2)) ?

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

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\frac{d}{d x} (\frac{ln ( x + 1 )}{4 x + 2})

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

Solution steps

\frac{d}{d x} (\frac{ln ( x + 1 )}{4 x + 2})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( ln ( x + 1 ) ) ( 4 x + 2 ) - \frac{d}{d x} ( 4 x + 2 ) ln ( x + 1 )}{( 4 x + 2 ) ^{2}}

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

\frac{d}{d x} (4 x + 2) = 4

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

Simplify

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

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

\int sec^{3} (4 x) d x

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

\frac{d}{d x} ((3 x + 1)^{6} 2 x - 5)

\int 2 x d x

\frac{d}{d r} (r^{3})

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