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

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

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

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

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

\frac{1}{2 x ^{2} + 2 x + 1}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1}{2 x ^{2} + 2 x + 1}

\frac{d}{d x} (x^{2} - 4 x + 9)

y^{^{''}} + 4 y^{^{'}} + 4 y = e^{- 2 x} + x^{2}

\frac{d y}{d x} = 13 x^{12} y

\frac{d}{d x} (arcsin (\frac{x - 2}{1}))

\int_{2}^{6} π (y - 2) 2 d y

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