What is the derivative of (arctan(x)dx) ?

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

What is the first derivative of (arctan(x)dx) ?

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

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

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

Solution steps

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

Treat

d

as a constant

Take the constant out:

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

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = arctan (x), g = x

= d (\frac{d}{d x} (arctan (x)) x + \frac{d x}{d x} arctan (x))

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

\frac{d x}{d x} = 1

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

Simplify

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

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

\frac{d}{d x} (\frac{x ^{2} + 1}{3 x ^{3} + 4 x})

\int (e^{x}) d x

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

x \to 3 lim (4 x^{2} - 2 x + 10)

\int 8 e^{x} d x

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