Differentiate each the following from first principles : (i) x sin x (

1.	Differentiate each the following from first principles : (i) x sin x (ii) x+cos x (iii) sin (2x−3) (iv) √sin 2x (v) sin xx (vi) cos xx (vii) x2 sin x (viii) √sin(3x+1) (ix) sin x+cos x
Answer» Differentiate each the following from first principles : $(i) x s i n x$ $(i i) x + c o s x$ $(i i i) s i n (2 x - 3)$ $(i v) \sqrt{s i n 2 x}$ $(v) \frac{s i n x}{x}$ $(v i) \frac{c o s x}{x}$ $(v i i) x^{2} s i n x$ $(v i i i) \sqrt{s i n (3 x + 1)}$ $(i x) s i n x + c o s x$

Differentiate each the following from first principles : (i) x sin x (ii) x+cos x (iii) sin (2x−3) (iv) √sin 2x (v) sin xx (vi) cos xx (vii) x2 sin x (viii) √sin(3x+1) (ix) sin x+cos x

Answer»

Differentiate each the following from first principles :

$(i) x s i n x$

$(i i) x + c o s x$

$(i i i) s i n (2 x - 3)$

$(i v) \sqrt{s i n 2 x}$

$(v) \frac{s i n x}{x}$

$(v i) \frac{c o s x}{x}$

$(v i i) x^{2} s i n x$

$(v i i i) \sqrt{s i n (3 x + 1)}$

$(i x) s i n x + c o s x$