Question

问个导数的运算,3Q刚学的：y=2^x*lnx2的X次乘以lnx的导数

Answer 1

若 f(x) = g(x)*t(x) ,且f(x),g(x),t(x)均可导,则

有 f'(x) = g'(x)*t(x) + g(x)*t'(x)

故 原题:

y=2^x*lnx

y'=(2^x)'*lnx + (2^x) * (lnx)'

=(2^x*ln 2) *lnx + (2^x) *(1/x)

=2^x*lnx*ln2+(2^x)/x