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Popular >

derivative of (arctan(3x)^2)

Solution

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

Solution

\frac{6 arctan ( 3 x )}{9 x ^{2} + 1}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (arctan (3 x)) = \frac{3}{9 x ^{2} + 1}

= 2 arctan (3 x) \frac{3}{9 x ^{2} + 1}

Simplify

2 arctan (3 x) \frac{3}{9 x ^{2} + 1} : \frac{6 arctan ( 3 x )}{9 x ^{2} + 1}

= \frac{6 arctan ( 3 x )}{9 x ^{2} + 1}

Popular Examples

tangent of f(x)= 8/(x+3),2 tangent of

f (x) = \frac{8}{x + 3}, 2

limit as x approaches 3+of sqrt(9-x^2)

x \to 3 + lim (9 - x^{2})

taylor 1/(x+5),0 taylor

\frac{1}{x + 5}, 0

integral from 0 to 5 of |5x-1|

\int_{0}^{5} ∣ 5 x - 1 ∣ d x

integral from 1 to 3 of (2x)

\int_{1}^{3} (2 x) d x

Frequently Asked Questions (FAQ)

What is the derivative of (arctan(3x)^2) ?
The derivative of (arctan(3x)^2) is (6arctan(3x))/(9x^2+1)
What is the first derivative of (arctan(3x)^2) ?
The first derivative of (arctan(3x)^2) is (6arctan(3x))/(9x^2+1)