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

The derivative of y=arctan(3x^2) is (6x)/(9x^4+1)

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

The first derivative of y=arctan(3x^2) is (6x)/(9x^4+1)

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derivative of

y = arctan (3 x^{2})

\frac{6 x}{9 x ^{4} + 1}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (3 x^{2}) = 6 x

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

Simplify

\frac{1}{( 3 x ^{2} ) ^{2} + 1} \cdot 6 x : \frac{6 x}{9 x ^{4} + 1}

= \frac{6 x}{9 x ^{4} + 1}

What is the derivative of y=arctan(3x^2) ?
The derivative of y=arctan(3x^2) is (6x)/(9x^4+1)
What is the first derivative of y=arctan(3x^2) ?
The first derivative of y=arctan(3x^2) is (6x)/(9x^4+1)