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