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CONTINUITY AND DIFFERENTIABILITY — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSCONTINUITY AND DIFFERENTIABILITY2 Marks
Question
Find the second order derivatives of the function given in Exercise:
$\text{e}^{6\text{x}}\cos3\text{x}$
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Answer

Let $\text{y}=\text{e}^{6\text{x}}\cos3\text{x}$
$\therefore\ \frac{\text{dy}}{\text{dx}}=6\text{e}^{6\text{x}}\cos3\text{x}-3\text{e}^{6\text{x}}\sin3\text{x}$
$\therefore\ \frac{\text{d}^2\text{y}}{\text{dx}^2}=36\text{e}^{6\text{x}}\cos3\text{x}-18\text{e}^{6\text{x}}\sin3\text{x}-18\text{e}^{6\text{x}}\sin3\text {x}-9\text{e}^{6\text{x}}\cos3\text{x}$
$=27\text{e}^{6\text{x}}\cos3\text{x}-36\text{e}^{6\text{x}}\sin3\text{x}=9\text{e}^{6\text{x}}(3\cos\text{x}-4\sin3\text{x})$

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