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Popular >

derivative of arctan(x^3-1)

Solution

\frac{d}{d x} (arctan (x^{3} - 1))

Solution

\frac{3 x ^{2}}{x ^{6} - 2 x ^{3} + 2}

Solution steps

\frac{d}{d x} (arctan (x^{3} - 1))

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{3 x ^{2}}{x ^{6} - 2 x ^{3} + 2}

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Frequently Asked Questions (FAQ)

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