# Exercises - Logarithmic Differentiation

1. Differentiate. Simplify your answers, as appropriate.

1. $y = (\ln x)^x$

2. $y = (x^2 - 3)^{\cos x}$

3. $y = \ln x^{2x} + (\ln x)^{2x} - \ln e^{x^2}$

4. $\displaystyle{y = \ln \left( \frac{e^{x^2-4}}{x-2} \right)}$

5. $y = (\cot^2 x^3) (\sec^2 x^3)$

6. $y = (\cos x^2)^{2x}$

7. $f(x) = (\tan x)^{\sin x}$

8. $y = \ln x^2 + (\ln x)^2 - \ln e^{x^2} + e^{x^2}$

9. $y = x^{2x+1}$

10. $y = 3^{\csc 5x}$

11. $y = (x^2+1)^{\ln x}$

12. $y = \ln (\sin x)^{\cos x}$

13. $y = (\ln x)^{\cos x}$