Differentiate w.r.t. x the function in Exercises 1 to 11.
3. \left(5x\right)^{3cos{2}x}.
4. {sin}^{-1}{\left(x\sqrt x\right)},0\le\ x\le1.
5. \frac{{cos}^{-1}{\frac{x}{2}}}{\sqrt{2x+7}},-2<x<2.
7. \left(log{x}\right)^{log{x}}, x>1.
8. cos{\left(acos{x}+bsin{x}\right)}, for some constant a and b.
9. \left(sin{x}-cos{x}\right)^{\left(sin{x}-cos{x}\right)}, \frac{\pi}{4}<x<\frac{3\pi}{4}.
10. x^x+x^a+a^x+a^a, for some fixed a>0 and x>0.
11. x^{x^2-3}+\left(x-3\right)^{x^2}, for x>3.
13. Find \frac{dy}{dx}, If y={sin}^{-1}{x}+{sin}^{-1}{\sqrt{1-x^2}},-1\le\ x\le1.
17. If x=a\left(cos{t}+tsin{t}\right) and y=a\left(sin{t}-tcos{t}\right), find \frac{d^2y}{dx^2}.
18. If f\left(x\right)=\left|x\right|^3, show that f”(x) exists for all real x and find it.