What is the derivative of y=(arctan(3x))2 ?

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

What is the first derivative of y=(arctan(3x))2 ?

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

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derivative of

y = (arctan (3 x)) 2

\frac{6}{9 x ^{2} + 1}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{6}{9 x ^{2} + 1}

y^{^{''}} - 9 y = e^{3 x}

f (x) = x^{\frac{2}{3}} (x^{2} - 4)

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

\frac{d}{d x} (y (θ, x) tan (θ))

y \frac{d y}{d x} - y^{3} = y^{2} ln (x)

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