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

1.	Differentiate each the following from first principles : (i) e−x (ii) e3x (iii) eax+b (iv) x ex (v) x2 ex (vi) ex2+1 (vii) e√2x (viii) e√ax+b (ix) a√x (x) 3x2
Answer» Differentiate each the following from first principles : $(i) e^{- x}$ $(i i) e^{3 x}$ $(i i i) e^{a x + b}$ $(i v) x e^{x}$ $(v) x^{2} e^{x}$ $(v i) e^{x^{2} + 1}$ $(v i i) e^{\sqrt{2 x}}$ $(v i i i) e^{\sqrt{a x + b}}$ $(i x) a^{\sqrt{x}}$ $(x) 3^{x^{2}}$

Differentiate each the following from first principles : (i) e−x (ii) e3x (iii) eax+b (iv) x ex (v) x2 ex (vi) ex2+1 (vii) e√2x (viii) e√ax+b (ix) a√x (x) 3x2

Answer»

Differentiate each the following from first principles :

$(i) e^{- x}$

$(i i) e^{3 x}$

$(i i i) e^{a x + b}$

$(i v) x e^{x}$

$(v) x^{2} e^{x}$

$(v i) e^{x^{2} + 1}$

$(v i i) e^{\sqrt{2 x}}$

$(v i i i) e^{\sqrt{a x + b}}$

$(i x) a^{\sqrt{x}}$

$(x) 3^{x^{2}}$