Question

高二数学求导：y=(x＾m+a＾m)(x＾n+a＾n)

Answer 1

y=(x^m+a^m)(x^n+a^n)

y'=(x^m+a^m)'(x^n+a^n)+(x^m+a^m)(x^n+a^n)'=m[x^(m-1)](x^n+a^n)+n[x^(n-1)](x^m+a^m)

y=[sin^4(3x)]*[cos^3(4x)]

y=[sin^4(3x)]'*[cos^3(4x)]+[sin^4(3x)]*[cos^3(4x)]'

=12[sin^3(3x)]*(cos3x)*[cos^3(4x)]-[sin^4(3x)]*12[cos^2(4x)]*(sin4x)

y=2[e^(x/2)+e^(-x/2)]

y'=2[(1/2)e^(x/2)-(1/2)e^(-x/2)]

=e^(x/2)-e^(-x/2)