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Question
Find the second order derivative of the function.
x . cos x
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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 × 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 x + sin x × 1] + [−sin x]
= −x cos x − sin x − sin x
= −x cos x + 2 sin x
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