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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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