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数学求导设y=f[(3x-2)/(3x+2)],f'(x)=arctanx^2,求dy/dx|x=0

题目详情
【数学】求导
设y=f[(3x-2)/(3x+2)],f'(x)=arctanx^2 ,求dy/dx|x=0
▼优质解答
答案和解析
y = ƒ[(3x-2)/(3x+2)]
= ƒ[(3x+2-4)/(3x+2)]
= ƒ[1-4/(3x+2)]
dy/dx = {arctan[(3x-2)/(3x+2)]²}[12/(3x+2)²]
dy/dx|(x=0) = {arctan[-2/2]²}[12/4] = 3π/4