Question

微积分求导

谢谢！

Answer 1

详情如图所示

有任何疑惑，欢迎追问

Answer 2

1、y=2^[3^(4^x)]
y'=2^[3^(4^x)]*ln2*[3^(4^x)]'
=2^[3^(4^x)]*ln2*[3^(4^x)]*ln3*(4^x)'
=2^[3^(4^x)]*ln2*[3^(4^x)]*ln3*(4^x)*ln4
=ln2*ln3*ln4*2^[3^(4^x)]*[3^(4^x)]*(4^x)
2、f(t)=te^t*cott
f'(t)=e^t*cott+te^t*cott+te^t*(-csc^2t)
=e^t*(cott+t*cott-t*csc^2t)
3、y=arctan[x-√(1+x^2)]
y'={1/{1+[x-√(1+x^2)]^2}}*[x-√(1+x^2)]'
={1/{1+[x-√(1+x^2)]^2}}*[1-x/√(1+x^2)]
=[√(1+x^2)-x]/{√(1+x^2)*{1+[x-√(1+x^2)]^2}}
=1/{√(1+x^2)*[√(1+x^2)+x+√(1+x^2)-x]}
=1/2(1+x^2)
4、F(x)=x*arcsec(x^3)
sec[F(x)/x]=x^3
cos[F(x)/x]=1/x^3
-sin[F(x)/x]*[F(x)/x]'=-3/x^4
sin[F(x)/x]*[F'(x)*x-F(x)]/x^2=3/x^4
F'(x)*x-F(x)=(3/x^2)*csc[F(x)/x]
F'(x)=(3/x^3)*csc[F(x)/x]+F(x)/x
=(3/x^3)*csc[arcsec(x^3)]+arcsec(x^3)
=(3/x^3)*[x^3/√(x^6-1)]+arcsec(x^3)
=3/√(x^6-1)+arcsec(x^3)

Answer 3