Using quotient rule, differentiable with respect to x(i) y = (secx + 1

1.	Using quotient rule, differentiable with respect to x(i) y = (secx + 1)/(secx - 1)(ii) y = (1 - tanx)/(1 + tanx)(iii) y = (secx - 1)/(secx + 1)
Answer» (i) dy/dx = ((secx - 1)secxtanx - (secx + 1)secxtanx)/(secx - 1)² = (-2secxtanx)/(secx - 1)² (ii) dy/dx ((1 + tanx)(-sec²x) - (1 - tanx)secx²x)/(1 + tanx)² = -2sec²x/(1 + tanx)² (iii) dy/dx = ((secx + 1)secxtanx - (secx - 1)secxtanx)/(secx + 1)² = 2secxtanx/(secx + 1)²

Using quotient rule, differentiable with respect to x(i) y = (secx + 1)/(secx - 1)(ii) y = (1 - tanx)/(1 + tanx)(iii) y = (secx - 1)/(secx + 1)

Answer»

(i) dy/dx = ((secx - 1)secxtanx - (secx + 1)secxtanx)/(secx - 1)²

= (-2secxtanx)/(secx - 1)²

(ii) dy/dx ((1 + tanx)(-sec²x) - (1 - tanx)secx²x)/(1 + tanx)²

= -2sec²x/(1 + tanx)²

(iii) dy/dx = ((secx + 1)secxtanx - (secx - 1)secxtanx)/(secx + 1)²

= 2secxtanx/(secx + 1)²

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