d/dx a^x,if a<0

Shouldn''t it be a^x * ln a ??? 

a^x=m
xln a=ln m
ln a=1/m(dm/dx)
[a^x/ln a] = dm/dx=d/dx a^x
 ANS

In JEE,  we don''t deal with power functions with base<0 as it oscillates between real and complex very frequently. Think of x=1, 1/4, 1/2, 1/8, 2...... out of these only two points are defined. So, base <0 isn''t there in jee syllabus. Don''t worry about it.

d/dx = x(a)^x-1