Determine the second derivative of [tex]y = \cos x \tan x[/tex].

f ( x ) = cos x t an x ( cos x t an x ) ′ = ( cos x ⋅ cos x s in x ​ ) ′ = ( s in x ) ′ = cos x ( cos x ) ′ = − s in x f ′′ ( x ) = − s in x δ x 2 δ 2 f ​ = − s in x

Answered by Anonymous | 2024-06-10

To find the second derivative of y = cos x tan x , we apply the product rule and find that the second derivative is given by y ′′ = − sin x sec 2 x + sin x sec x . This involves calculating the first derivative using the product rule and then differentiating again. The final result combines terms derived from both parts of the product rule.
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Answered by Anonymous | 2024-12-23