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Popular >

derivative of arctan(3x^3)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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