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.

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