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Question
Find the second order derivative of the function.
x . cos x
Solution
Let, y = x cos x
Differentiating both sides with respect to x,
`dy/dx = x d/dx cos x + cos x d/dx (x)`
= x (- sin x) + cos x `xx` 1
= - x sin x + cos x
Differentiating both sides again with respect to x,
`(d^2 y)/dx^2 = - [x d/dx sin x + sin x d/dx (x)] + d/dx cos x`
= `- [x cos + sin x xx 1] + [- sin x]`
= - x cos x - sin x - sin x
= - x cos x + 2 sin x
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