Question

find the dy/dx of y=3^(x^2)

Answer 1

put ln to both sides :
ln y = ln(3^(x^2))

Answer 2

or :
ln y = x^2 ln3
then take derivative :
1/y dy = 2xln3 dx
dy/dx = 2xln3 * y

Answer 3

substitute back y = 3^(x^2)
so, dy/dx = 2xln3 * 3^(x^2)