Chapter 3.9, Problem 87E

Explain why or why not Determine whether the following statements are true and give an explanation or counterexample

  a.    The derivative of log₂9 is 1/(9 ln 2).

  b.    In (x + 1) + ln (x – 1) = ln (x² – 1), for all x

  c.    The exponential function 2^{x + 1} can be written in base e as e^{2 ln(x +1)}

  d.     $\frac{d}{dx}\left({\sqrt{2}}^x\right)=x{\sqrt{2}}^{x-1}$

  e.     $\frac{d}{dx}\left(x^{\sqrt{2}}\right)={\sqrt{2x}}^{\sqrt{2}-1}$

  f.     ${\left(4x-1\right)}^{\ln x}=x^{\ln \left(4x+1\right)}$