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positive96
@positive96
July 2022
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помогите решить 1860
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Удачник66
Verified answer
Z = u^v; u = sin x; v = cos x
dz/dx = (dz/du)*(du/dx) + (dz/dv)*(dv/dx)
Находим каждую производную отдельно
dz/du=v*u^(v-1)=cos x*(sin x)^(cos x - 1)=cos x/sin x*(sin x)^(cos x)=ctg x*(sin x)^(cos x)
dz/dv = v^y*ln |u| = (sin x)^(cos x)*ln |sin x|
du/dx = cos x
dv/dx = -sin x
Подставляем
dz/dx = (sin x)^(cos x)*(ctg x*cos x - ln |sin x|*sin x)
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Answers & Comments
Verified answer
Z = u^v; u = sin x; v = cos xdz/dx = (dz/du)*(du/dx) + (dz/dv)*(dv/dx)
Находим каждую производную отдельно
dz/du=v*u^(v-1)=cos x*(sin x)^(cos x - 1)=cos x/sin x*(sin x)^(cos x)=ctg x*(sin x)^(cos x)
dz/dv = v^y*ln |u| = (sin x)^(cos x)*ln |sin x|
du/dx = cos x
dv/dx = -sin x
Подставляем
dz/dx = (sin x)^(cos x)*(ctg x*cos x - ln |sin x|*sin x)