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

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

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

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

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derivative of

f (x) = 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}

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

f (x) = \frac{2 x}{x ^{2} + 1}, at x = 1

\int 2 x (x^{2} + 5)^{3} d x

x \to - 1 lim (\frac{6 x + 5}{5 x - 6})

\frac{\partial}{\partial x} \frac{10 3 ( 5 x ) ^{2}}{3}

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