What is the derivative of y=arctan(2x) ?

The derivative of y=arctan(2x) is 2/(4x^2+1)

What is the first derivative of y=arctan(2x) ?

The first derivative of y=arctan(2x) is 2/(4x^2+1)

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derivative of

y = arctan (2 x)

\frac{2}{4 x ^{2} + 1}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{2}{4 x ^{2} + 1}

cos (θ), sin (2 θ)

\frac{\partial}{\partial x} (sin (5 x + 2 y))

\int e^{t} + 2 t + ln (t) d t

\int \frac{1}{x ^{2} + 2 x - 8} d x

\frac{d}{d x} (- sin (2 x) \cdot 2)

What is the derivative of y=arctan(2x) ?
The derivative of y=arctan(2x) is 2/(4x^2+1)
What is the first derivative of y=arctan(2x) ?
The first derivative of y=arctan(2x) is 2/(4x^2+1)