What is the derivative of (arctan(x)^3) ?

The derivative of (arctan(x)^3) is (3arctan^2(x))/(x^2+1)

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

The first derivative of (arctan(x)^3) is (3arctan^2(x))/(x^2+1)

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\frac{d}{d x} ((arctan (x))^{3})

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

Solution steps

\frac{d}{d x} ((arctan (x))^{3})

Apply the chain rule:

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

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

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

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

Simplify

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

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

What is the derivative of (arctan(x)^3) ?
The derivative of (arctan(x)^3) is (3arctan^2(x))/(x^2+1)
What is the first derivative of (arctan(x)^3) ?
The first derivative of (arctan(x)^3) is (3arctan^2(x))/(x^2+1)