1. y=2^x + 2^3x ;
2. z=3√x e^-x ;
3. v=ln √(1+x/1-x) .
y' = 2^x*ln 2 + 2^(3x)*ln 2*3 = ln 2*(2^x + 3*2^(3x))
2) z = 3sqrt(x)e^(-x)
[m]z' = \frac{3e^{-x}}{2*\sqrt{x}} - 3\sqrt{x}*e^{-x} = \frac{3e^{-x}}{\sqrt{x}}*(\frac{1}{2} - x)[/m]
3) [m]v = ln \sqrt{\frac{1+x}{1-x}}[/m]
[m]v' = \sqrt{\frac{1-x}{1+x}}*\frac{1}{2}*\sqrt{\frac{1-x}{1+x}}*\frac{1-x - (1+x)(-1)}{(1-x)^2} =[/m]
[m]= \frac{1}{2}*\frac{1-x}{1+x}*\frac{2}{(1-x)^2} = \frac{1}{2}*2*\frac{1-x}{(1+x)(1-x)^2}= \frac{1}{(1+x)(1-x)} = \frac{1}{1-x^2}[/m]