What is the derivative of 4arctan(2x) ?

The derivative of 4arctan(2x) is 8/(4x^2+1)

What is the first derivative of 4arctan(2x) ?

The first derivative of 4arctan(2x) is 8/(4x^2+1)

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\frac{d}{d x} (4 arctan (2 x))

\frac{8}{4 x ^{2} + 1}

Solution steps

\frac{d}{d x} (4 arctan (2 x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \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

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

Simplify

4 \cdot \frac{1}{( 2 x ) ^{2} + 1} \cdot 2 : \frac{8}{4 x ^{2} + 1}

= \frac{8}{4 x ^{2} + 1}

\frac{d y}{d x} = \frac{x - 2}{y + 1}

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

\int_{0}^{1} arctan (1) d x

\frac{d}{d x} (e^{s i n (x)} - 1)

\int_{3}^{13} x d x

What is the derivative of 4arctan(2x) ?
The derivative of 4arctan(2x) is 8/(4x^2+1)
What is the first derivative of 4arctan(2x) ?
The first derivative of 4arctan(2x) is 8/(4x^2+1)