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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (3 x^{2} - x) = 6 x - 1

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

Simplify

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

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

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