用对数求导法怎么做?
1个回答
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y = [(3-x)^4√(x+2)]/(x+5)^5
lny = ln[(3-x)^4√(x+2)]/(x+5)^5
= 4*ln(3-x) + 1/2*ln(x+2) - 5*ln(x+5)
【取对数求导法: [lny]'=y'/y ==> y'= y*[lny]'】
y' = y*[lny]'
= [(3-x)^4√(x+2)]/(x+5)^5 * [ 4*ln(3-x) + 1/2*ln(x+2) - 5*ln(x+5)]'
= [(3-x)^4√(x+2)]/(x+5)^5 * [ -4/(3-x) + 1/2(x+2) - 5/(x+5)]
lny = ln[(3-x)^4√(x+2)]/(x+5)^5
= 4*ln(3-x) + 1/2*ln(x+2) - 5*ln(x+5)
【取对数求导法: [lny]'=y'/y ==> y'= y*[lny]'】
y' = y*[lny]'
= [(3-x)^4√(x+2)]/(x+5)^5 * [ 4*ln(3-x) + 1/2*ln(x+2) - 5*ln(x+5)]'
= [(3-x)^4√(x+2)]/(x+5)^5 * [ -4/(3-x) + 1/2(x+2) - 5/(x+5)]
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