​ Find dy/dx if (a) x = a(t - 1/t), y = a(t + 1/t)1 ​

Question

Find \(\frac{dy}{dx}\) if 

(a) x = a(t - \(\frac{1}{t}\)), y = a(t + \(\frac{1}{t}\))1

(b) x = e^2t , y = log(2t + 1) 

(c) x = log(1 + t), y = \(\frac{1}{1 + t}\)

(d) x = log t, y = \(\frac{1}{t}\)

Answer 1

(a) Given x = a(t - \(\frac{1}{t}\)), y = a(t + \(\frac{1}{t}\))1

Differentiate both w.r.t

(b) Given x = e^2t, y = log(2t + 1) 

Differentiate both w.r.t we get

(c) Given x = log (1+t), y = \(\frac{1}{1 + t}\)

Differentiate both w.r.t x t, we get

(d) Given x = log t, y = \(\frac{1}{t}\)

Differentiate both w.r.t t, we get