What is the derivative of arctan(2x^2-4) ?

The derivative of arctan(2x^2-4) is (4x)/(4x^4-16x^2+17)

What is the first derivative of arctan(2x^2-4) ?

The first derivative of arctan(2x^2-4) is (4x)/(4x^4-16x^2+17)

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

\frac{4 x}{4 x ^{4} - 16 x ^{2} + 17}

Solution steps

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

Apply the chain rule:

\frac{1}{( 2 x ^{2} - 4 ) ^{2} + 1} \frac{d}{d x} (2 x^{2} - 4)

= \frac{1}{( 2 x ^{2} - 4 ) ^{2} + 1} \frac{d}{d x} (2 x^{2} - 4)

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

= \frac{1}{( 2 x ^{2} - 4 ) ^{2} + 1} \cdot 4 x

Simplify

\frac{1}{( 2 x ^{2} - 4 ) ^{2} + 1} \cdot 4 x : \frac{4 x}{4 x ^{4} - 16 x ^{2} + 17}

= \frac{4 x}{4 x ^{4} - 16 x ^{2} + 17}

y^{^{''}} - 8 y^{^{'}} + 16 = 0

x \to π lim ((π - x) cot (x))

(e^{- 1}) (sin (2 t))

e^{8 x} cos (11 x)

\int X^{- 1} d X

What is the derivative of arctan(2x^2-4) ?
The derivative of arctan(2x^2-4) is (4x)/(4x^4-16x^2+17)
What is the first derivative of arctan(2x^2-4) ?
The first derivative of arctan(2x^2-4) is (4x)/(4x^4-16x^2+17)