求导 y = [x + (x + (sin(x))^2)^5]^7 我求的很复杂,一直不对.
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![求导 y = [x + (x + (sin(x))^2)^5]^7 我求的很复杂,一直不对.](/uploads/image/z/9414429-69-9.jpg?t=%E6%B1%82%E5%AF%BC+y+%3D+%5Bx+%2B+%28x+%2B+%28sin%28x%29%29%5E2%29%5E5%5D%5E7+%E6%88%91%E6%B1%82%E7%9A%84%E5%BE%88%E5%A4%8D%E6%9D%82%2C%E4%B8%80%E7%9B%B4%E4%B8%8D%E5%AF%B9.)
求导 y = [x + (x + (sin(x))^2)^5]^7 我求的很复杂,一直不对.
求导 y = [x + (x + (sin(x))^2)^5]^7 我求的很复杂,一直不对.
求导 y = [x + (x + (sin(x))^2)^5]^7 我求的很复杂,一直不对.
解答如下(修改):
y'=7[x+(x+(sinx)^2)^5]^6*[1+5(x+(sinx)^2)^4]*(1+sin2x)
原式= [x + (x + (sin(x))^2)^5]^7
求导得 y'={[x + (x + (sin(x))^2)^5]^7}'
=7[x + (x + (sin(x))^2)^5]^6*[x + (x + (sin(x))^2)^5]'
=7[x + (x + (sin(x))^2)^5]^6*[(x)'+(x + (sin(x))^2)^5']
=7[x ...
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原式= [x + (x + (sin(x))^2)^5]^7
求导得 y'={[x + (x + (sin(x))^2)^5]^7}'
=7[x + (x + (sin(x))^2)^5]^6*[x + (x + (sin(x))^2)^5]'
=7[x + (x + (sin(x))^2)^5]^6*[(x)'+(x + (sin(x))^2)^5']
=7[x + (x + (sin(x))^2)^5]^6*{1+[5(x + (sin(x))^2)^4]*[x + (sin(x))^2]'}
=7[x + (x + (sin(x))^2)^5]^6*{1+[5(x + (sin(x))^2)^4]*[1 + 2cos(x)]}
=7[x + (x + (sin(x))^2)^5]^6*{1+[5(x + (sin(x))^2)^4]*[1 + 2sin(x)cos(x)]}
收起
y'={[x + (x + (sin(x))^2)^5]^7}'
=7[x + (x + (sin(x))^2)^5]^6*[x + (x + (sin(x))^2)^5]'
=7[x + (x + (sin(x))^2)^5]^6*[(x)'+(x + (sin(x))^2)^5']
=7[x + (x + (sin(x))^2)^5]^6*{1+[5(x + (sin(...
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y'={[x + (x + (sin(x))^2)^5]^7}'
=7[x + (x + (sin(x))^2)^5]^6*[x + (x + (sin(x))^2)^5]'
=7[x + (x + (sin(x))^2)^5]^6*[(x)'+(x + (sin(x))^2)^5']
=7[x + (x + (sin(x))^2)^5]^6*{1+[5(x + (sin(x))^2)^4]*(x + (sin(x))^2)'}
=7[x + (x + (sin(x))^2)^5]^6*{1+[5(x + (sin(x))^2)^4]*(1+2sinx[sin(x)]')}
=7[x + (x + (sin(x))^2)^5]^6*{1+[5(x + (sin(x))^2)^4]*(1+2sin(x)cos(x))}
=7[x + (x + (sin(x))^2)^5]^6*{1+[5(x + (sin(x))^2)^4]*(1+sin(2x))}
PS:楼上两位都求错了。
收起
这个函数还挺长啊
设a=x+(sinx)^2;
b=a'=1+sin2x
则原式的导数是:
(1+b*5a^4)*7(x+a^5)^6
y = [x + (x + (sin(x))^2)^5]^7
y'={[x + (x + (sin(x))^2)^5]^7}'
=7[x + (x + (sin(x))^2)^5]^6*[x + (x + (sin(x))^2)^5]'
=7[x + (x + (sin(x))^2)^5]^6*[(x)'+(x + (sin(x))^2)^5']
=7[x +...
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y = [x + (x + (sin(x))^2)^5]^7
y'={[x + (x + (sin(x))^2)^5]^7}'
=7[x + (x + (sin(x))^2)^5]^6*[x + (x + (sin(x))^2)^5]'
=7[x + (x + (sin(x))^2)^5]^6*[(x)'+(x + (sin(x))^2)^5']
=7[x + (x + (sin(x))^2)^5]^6*[1+5(x + (sin(x))^2)^4]*[x + (sin(x))^2]'
=7[x + (x + (sin(x))^2)^5]^6*[1+5(x + (sin(x))^2)^4]*[1+2sin(x)]*sin(x)'
=7[x + (x + (sin(x))^2)^5]^6*[1+5(x + (sin(x))^2)^4]*[1+2sin(x)]*cosx
收起