Differentiate: y = 2 ^ x

y = 2 ^ x

take ln of both sides

ln( y) = ln (2 ^ x)

using the log rules we can bring the power of x down in front of the ln

ln( y ) = x*ln(2)

differentiate both sides wrt x

( 1 / y ) * dy / dx = ln(2)

dy / dx = y*ln(2)   ==> rememer  y = 2 ^ x

dy / dx = ln(2) * 2 ^ x