Find the second order derivatives of the function given in Exerci… - Vidyadip

Question

Find the second order derivatives of the function given in Exercise:
$\text{e}^\text{x}\sin5\text{x}$

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Answer

Let $\text{y}=\text{e}^\text{x}\sin5\text{x}$
$\therefore\ \frac{\text{dy}}{\text{dx}}=\text{e}^\text{x}\sin\text{x}+5\text{e}^\text{x}\cos5\text{x}$
$\therefore\ \frac{\text{d}^2\text{y}}{\text{dx}^2}=\text{e}^\text{x}\sin5\text{x}+5\text{e}^\text{x}\cos5\text{x}+5\text{e}^\text{x}\cos5\text {x}-25\text{ e}^\text{x}\sin5\text{x}$
$=10\text{e}^\text{x}\cos5\text{x}-24\text{e}^\text{x}\sin5\text{x}=2\text{e}^\text{x}(5\cos5\text{x}-12\sin5\text{x})$

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