What is the derivative of arctan(3x+2) ?

The derivative of arctan(3x+2) is 3/(9x^2+12x+5)

What is the first derivative of arctan(3x+2) ?

The first derivative of arctan(3x+2) is 3/(9x^2+12x+5)

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\frac{d}{d x} (arctan (3 x + 2))

\frac{3}{9 x ^{2} + 12 x + 5}

Solution steps

\frac{d}{d x} (arctan (3 x + 2))

Apply the chain rule:

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

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

\frac{d}{d x} (3 x + 2) = 3

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

Simplify

\frac{1}{( 3 x + 2 ) ^{2} + 1} \cdot 3 : \frac{3}{9 x ^{2} + 12 x + 5}

= \frac{3}{9 x ^{2} + 12 x + 5}

\frac{1}{5 + 2 x}

f (t) = \frac{5 t + 300}{t ^{2} + 25}

\int \frac{2 e ^{2 x}}{e ^{2 x} + 8 e ^{x} + 15} d x

\int \frac{1}{x ^{2} x ^{2} + 5} d x

\int sin (x) + 9 d x

What is the derivative of arctan(3x+2) ?
The derivative of arctan(3x+2) is 3/(9x^2+12x+5)
What is the first derivative of arctan(3x+2) ?
The first derivative of arctan(3x+2) is 3/(9x^2+12x+5)