) y=ex Differentiating with respect to x, we get ⇒
dy
dx
=ex Again differentiating with respect to x, we get ⇒
d2y
dx2
=ex ......(1) Again, y=ex Taking log both sides, we get ⇒log‌y=log⇒ex ⇒log‌y=x‌log‌e(∵log‌mn=n‌log‌m) ⇒log‌y=x(∵log‌e=1) ⇒x=log‌y Differentiating with respect to y, we get ⇒
dx
dy
=
1
y
Again differentiating with respect to y, we get ⇒
d2x
dy2
=
−1
y2
.......(2) Multiplying equation (1) and (2), we get (