设y=(x+1)^2(x+2)^3 / √x+3(x+4)求y'文字描述...“.X+1的括号平方乘于x+2的括号3次方比更号下x+3乘于括号x+4”
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 23:22:20
![设y=(x+1)^2(x+2)^3 / √x+3(x+4)求y'文字描述...“.X+1的括号平方乘于x+2的括号3次方比更号下x+3乘于括号x+4”](/uploads/image/z/14657632-16-2.jpg?t=%E8%AE%BEy%3D%28x%2B1%29%5E2%28x%2B2%29%5E3+%2F+%E2%88%9Ax%2B3%28x%2B4%29%E6%B1%82y%27%E6%96%87%E5%AD%97%E6%8F%8F%E8%BF%B0...%E2%80%9C.X%2B1%E7%9A%84%E6%8B%AC%E5%8F%B7%E5%B9%B3%E6%96%B9%E4%B9%98%E4%BA%8Ex%2B2%E7%9A%84%E6%8B%AC%E5%8F%B73%E6%AC%A1%E6%96%B9%E6%AF%94%E6%9B%B4%E5%8F%B7%E4%B8%8Bx%2B3%E4%B9%98%E4%BA%8E%E6%8B%AC%E5%8F%B7x%2B4%E2%80%9D)
设y=(x+1)^2(x+2)^3 / √x+3(x+4)求y'文字描述...“.X+1的括号平方乘于x+2的括号3次方比更号下x+3乘于括号x+4”
设y=(x+1)^2(x+2)^3 / √x+3(x+4)求y'
文字描述...“.X+1的括号平方乘于x+2的括号3次方
比更号下x+3乘于括号x+4”
设y=(x+1)^2(x+2)^3 / √x+3(x+4)求y'文字描述...“.X+1的括号平方乘于x+2的括号3次方比更号下x+3乘于括号x+4”
取对数求导法:
(lny)'=y'/y
∴ y' = y*(lny)'
y' = y*(lny)'
= y * { 2ln(x+1)+3ln(x+2) - ln(x+4) -1/2*ln(x+3)}'
= y * { 2/(x+1)+3/(x+2) - 1/(x+4) -1/[2(x+3)] }
= (x+1)^2(x+2)^3 / √x+3(x+4) * { 2/(x+1)+3/(x+2) - 1/(x+4) -1/[2(x+3)] }
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