1) f(x) = 3ln(2x+1)
f'(x) = 6/(2x+1)
f'(0) = 6
2) f(x) = 5x+lnx
f'(x) = 5+1/x
f'(1) = 5 +1 = 6
3) y = x²lnx
y'=2xlnx + x²*1/х
y'(1) = 0 + 1 = 1
4) y = ln²5x
y'= 2ln5x*1/5x*5 = 2ln5x/x
5) y = ln((x-2)/(x+2) )
y' = (x+2)/(x-2) * ((x-2)/(x+2) )'= (x+2)/(x-2) * (x+2 -x+2)/(x+2)²=
=(x+2)/(x-2) * 4/(x+2)² = 4/(x²-4)
6) y = 3^(2x² -4)
y'=3^(2x²-4)*ln3*(2x² -4)' = 3^(2x²-4)*ln3*4x
y'(0) = 0
7) f(x) = (1/3)^(x² -3x)
f'(x) = (1/3)^(x² -3x) * ln(1/3)*(2x-3)
8) y = 3^x * x³
y'=( 3^x)' * x³ + 3^x * (x³)' = 3^x*ln3*x³ + 3^x*3x²
y'(0) = 0
9)f(x) = (e^2x - e^-2x)/2
f'(x) = 2e^2x/2 +2e^-2x/2=e^2x +e^-2x
f'(0) = 1 +1 = 2
10)y = lnSin⁴x/4
y' =1/Sin⁴x/4 * 4Sin³x/4 * 1/4