Differentiate each of the following from first principles:(i) sin 2x(i – InterviewSolution

1.	Differentiate each of the following from first principles:(i) sin 2x(ii) sin xx(iii) cos xx(iv) x2 sin x(v) sin (3x+1)(vi) sin x + cos x(vii) x2 ex(viii) ex2+1(ix) e2x(x) eax+b(xi) ax(x) 3x2
Answer» Differentiate each of the following from first principles: (i) $\sqrt{\sin 2 x}$ (ii) $\frac{\sin x}{x}$ (iii) $\frac{\cos x}{x}$ (iv) x² sin x (v) $\sqrt{\sin (3 x + 1)}$ (vi) sin x + cos x (vii) x² e^x (viii) $e^{x^{2} + 1}$ (ix) $e^{\sqrt{2 x}}$ (x) $e^{\sqrt{a x + b}}$ (xi) $a^{\sqrt{x}}$ (x) $3^{x^{2}}$

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