Find the derivative of 2x+33x+2 by first principle.
Let f(x) = 2x+33x+2
Then, f(x+h)=2(x+h)+33(x+h)+2
∴f′(x)=limh→02(x+h)+33(x+h)+2−2x+33x+2h
=limh→0(2x+3+2h)(3x+2)−(2x+3)(3x+2+3h)h(3x+2)(3x+2+3h)
=limh→0(2x+3)(3x+2)+2h(3x+2)−(2x+3)(3x+2)−3h(2x+3)h(3x+2)(3x+2+3h)
=limh→0h(6x+4−6x−9)h(3x+2)(3x+2+3h)⇒f′(x)=limh→0−5(3x+2)(3x+2+3h)
=−5(3x+2)2