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Popular >

derivative of y=(arctan(3x))^2

Solution

derivative of

y = (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

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\frac{\partial}{\partial x} (y cos (x - y) - z)

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\int (x^{4} (5 - x^{2})) d x

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x \to 1000 lim (18 π^{2})

(\partial)/(\partial x)(x(2x-y^3))

\frac{\partial}{\partial x} (x (2 x - y^{3}))

Frequently Asked Questions (FAQ)

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