Question

if t=e^x. and y=t²-1
then Dy/Dx=????????
in t =1

Answer 1

$\textbf{Answer :}$

Given that,

t = eˣ

or, x = logt ...(i)

and

y = t² - 1 ...(ii)

Now, differentiating both sides of (i) and (ii) with respect to t, we get

dx/dt = 1/t

dy/dt = 2t

So, dx/dy

= (dx/dt)/(dy/dt)

= (1/t)/(2t)

= 1/(2t²)

So, dx/dy at t = 1 be

= 1/(2 × 1²)

= 1/(2 × 1)

= 1/2

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