find \( \frac{d y}{d x} \) 2) \( y=\sec ^{2}\left(3 x^{2}\right. \) 3) \( y \)

Find the first order derivative with respect to \( x \) for \( y=\sec^{2}(3x^{2}) \). Evaluate the derivative by following steps: - step0: Evaluate the derivative: \(y^{\prime}=\frac{d}{dx}\left(\sec^{2}\left(3x^{2}\right)\right)\) - step1: Use differentiation rules: \(y^{\prime}=\frac{d}{dg}\left(g^{2}\right)\times \frac{d}{dx}\left(\sec\left(3x^{2}\right)\right)\) - step2: Find the derivative: \(y^{\prime}=2g\times \frac{d}{dx}\left(\sec\left(3x^{2}\right)\right)\) - step3: Calculate: \(y^{\prime}=2g\times 6\sec\left(3x^{2}\right)\tan\left(3x^{2}\right)\times x\) - step4: Substitute back: \(y^{\prime}=2\sec\left(3x^{2}\right)\times 6\sec\left(3x^{2}\right)\tan\left(3x^{2}\right)\times x\) - step5: Multiply the terms: \(y^{\prime}=12\sec\left(3x^{2}\right)\sec\left(3x^{2}\right)\tan\left(3x^{2}\right)\times x\) - step6: Calculate: \(y^{\prime}=12\sec^{2}\left(3x^{2}\right)\tan\left(3x^{2}\right)\times x\) - step7: Reorder the terms: \(y^{\prime}=12x\sec^{2}\left(3x^{2}\right)\tan\left(3x^{2}\right)\) The first-order derivative of \( y = \sec^{2}(3x^{2}) \) with respect to \( x \) is \( y' = 12x\sec^{2}(3x^{2})\tan(3x^{2}) \).