Find the derivative of $∣ ∣ 2 x^{2} - 3 ∣ ∣$ with respect $x .$

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Solution

We have,
$\begin{matrix} y = ∣ ∣ 2 x^{2} - 3 ∣ ∣ y = 2 ∣ ∣ ∣ x^{2} - \frac{3}{2} ∣ ∣ ∣ y = 2 (x^{2} - \frac{3}{2}) x \in (- \infty, - \sqrt{\frac{3}{2}}] \cup [\sqrt{\frac{3}{2}}, \infty) y = 2 (\frac{3}{2} - x^{2}) x \in (- \sqrt{\frac{3}{2}}, \sqrt{\frac{3}{2}}) \frac{d y}{d x} = 4 x x \in (- \infty, - \sqrt{\frac{3}{2}}] \cup [\sqrt{\frac{3}{2}}, \infty) = - 4 x x \in (- \sqrt{\frac{3}{2}}, \sqrt{\frac{3}{2}}) \end{matrix}$

Hence, this is the answer.

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