Question

d/dx [(3x+2)^n +(2x+3)^m]

Answer 1

For d/dx (3x+2)^n, let

u(x) = 3x + 2
f(u(x)^n)= u^n
df/dx = (df/du)*(du/dx) = 3*n*u^(n-1)
= 3n*(3x+2)^(n-1)

For d/dx(2x+3)^m,
Let v(x) = 2x +3
g(v(x)^m) = v^m
dg/dx = (dg/dv)*(dv/dx) = 2 mv^(m-1)

Add the two terms

d/dx [(3x+2)^n +(2x+3)^m]
= 3n*(3x+2)^(n-1) + 2m*(2x+3)^(m-1)