19. Find the derivatives (differential coefficients of the following functions w.r.t. x ):
(i) $$10 x^5$$
(ii) $$2 x-\frac{3}{4}$$
(iii) $$4 \sqrt{x}-2$$
(iv) $$3 {cosec} x$$
20. Find the d.c. of $$x^3 \tan x$$ w.r.t. $$x$$.
21. Differentiate the following functions, $$x^{-3}$$
22. Differentiate the following functions, $$\sqrt[3]{x}$$
23. Differentiate the following functions, $$\frac{1}{x}$$
24. Differentiate the following functions, $$\frac{1}{\sqrt{x}}$$
25. Differentiate the following functions, $$3 x^{-5}$$
26. Differentiate the following functions, $$\frac{1}{5 x}$$
27. Differentiate the following functions, $$\sqrt[3]{x^2}$$
28. Find the derivative of $$f(x)=x^2-2$$ at $$x=10$$.
29. Find the derivative of $$f(x)=\cos x$$ at $$x=0$$.
30. Find the derivative of $$f(x)=\tan x$$ at $$x=0$$.
31. The differentiation of $$e^x$$ with respect to x is $$e^x$$.
32. The differentiation of $$a^x(a>0, a \neq 1)$$ with respect to x is $$a^x \log _e a$$.
33. The differentiation of $$\log _a x(a>0, a \neq 1)$$ with respect to x is $$\frac{1}{x \log _e a}$$ i.e., $$\frac{d}{d x}\left(\log _a x\right)=\frac{1}{x \log _e a}$$.
34. The differentiation of $$\cos x$$ with respect to x is $$-\sin \mathrm{x}$$ i.e., $$\frac{d}{d x}(\cos x)=-\sin x$$.
35. Differentiate each of the following first principal. $$k x^n$$.
36. Differentiate each of the following first principal $$x^2+x+3$$.
37. Differentiate each of the following first principal $$x^3+4 x^2+3 x+2$$.