F (x) = sinx+cosx/sinx-cosx производная

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Алгебра

Евтихий

17 ноября, 21:08

F (x) = sinx+cosx/sinx-cosx производная

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Элла · Answer 1

f′ (x) = (sin (x) + cos (x) / sin (x) - cos (x)) ′ = = (sin (x) + cos (x)) ′ ⋅ (sin (x) - cos (x)) - (sin (x) + cos (x)) ⋅ (sin (x) - cos (x)) ′ / (sin (x) - cos (x)) ^ 2 = = ((sin (x)) ′ + (cos (x)) ′) ⋅ (sin (x) - cos (x)) - (sin (x) + cos (x)) ⋅ ((sin (x)) ′ - (cos (x)) ′) / (sin (x) - cos (x)) ^ 2 = = (cos (x) + (-sin (x))) ⋅ (sin (x) - cos (x)) - (sin (x) + cos (x)) ⋅ (cos (x) - (-sin (x))) / (sin (x) - cos (x)) ^ 2