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Question
Find the second order derivative of the function.
ex sin 5x
Solution
Let, y = ex sin 5x
`dy/dx = e^x d/dx sin 5x + sin 5x d/dx e^x`
`= e^x. cos 5x. 5 + sin5x. e^x`
`= e^x [5 cos5x + sin 5x]`
`(d^2y)/dx^2 = e^x [5(-sin 5 x). 5 + cos 5x .5] + [5 cos 5x + sin 5x] e^x`
`= e^x [-25 sin 5x + 5cos 5x + 5 cos 5x + sin 5x]`
`= e^x [10 cos 5x - 24 sin 5x]`
`= 2e^x [5 cos 5x - 12 sin 5x]`
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