求下列函数的导数 y=(1+x^2/1-x^2)^2y=【(1+x^2)/(1-x^2)】^2
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求下列函数的导数 y=(1+x^2/1-x^2)^2y=【(1+x^2)/(1-x^2)】^2
求下列函数的导数 y=(1+x^2/1-x^2)^2
y=【(1+x^2)/(1-x^2)】^2
求下列函数的导数 y=(1+x^2/1-x^2)^2y=【(1+x^2)/(1-x^2)】^2
首先记住公式[f(g(x))]'=f'(g(x))*g'(x)
然后设a=(1+x^2)/(1-x^2),y=f(a)
y=f(a)=a^2
f'(a)=2a=2(1+x^2)/(1-x^2)
然后设b=1-x^2,a=g(b)
a=g(b)=(2-b)/b=2/b-1
g'(b)=-2/b^2=-2/(1-x^2)^2
b'=-2x
a'=[g(b)]'=g'(b)*b'=[-2/(1-x^2)^2]*(-2x)=4x/(1-x^2)^2
y'=[f(a)]'=f'(a)*a'=[2(1+x^2)/(1-x^2)]*[4x/(1-x^2)^2]=8x(1+x^2)/(1-x^2)^3
所以y'=8x(1+x^2)/(1-x^2)^3
y′
=2[(1+x^2)/(1-x^2)][(1+x^2)/(1-x^2)]′
=2[(1+x^2)/(1-x^2)][(1+x^2)′(1-x^2)-(1+x^2)(1-x^2)′]/(1-x^2)^2
=2[(1+x^2)/(1-x^2)][2x(1-x^2)+2x(1+x^2)]/(1-x^2)^2
=8x(1+x^2)/(1-x^2)^3。...
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y′
=2[(1+x^2)/(1-x^2)][(1+x^2)/(1-x^2)]′
=2[(1+x^2)/(1-x^2)][(1+x^2)′(1-x^2)-(1+x^2)(1-x^2)′]/(1-x^2)^2
=2[(1+x^2)/(1-x^2)][2x(1-x^2)+2x(1+x^2)]/(1-x^2)^2
=8x(1+x^2)/(1-x^2)^3。
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