Maharashtra State BoardHSC Commerce 12th Board Exam
Advertisement Remove all ads

Find d2ydx2, if y = 2at, x = at2 - Mathematics and Statistics

Sum

Find `("d"^2"y")/"dx"^2`, if y = 2at, x = at2

Advertisement Remove all ads

Solution

x = at

Differentiating both sides w.r.t. t, we get

`"dx"/"dt" = "a" "d"/"dx" ("t"^2) = "a"("2t")`

∴ `"dx"/"dt" = "2at"`      ....(i)

y = 2at

Differentiating both sides w.r.t. t, we get

`"dy"/"dt" = "2a" "d"/"dt" ("t")`

∴ `"dy"/"dt"` = 2a

∴ `"dy"/"dx" = ("dy"/"dt")/("dx"/"dt") = "2a"/"2at" = 1/"t"`

Again, differentiating both sides w.r.t. x, we get

`("d"^2"y")/"dx"^2 = (-1)/"t"^2 * "dt"/"dx" = (-1)/"t"^2 xx 1/"2at"`     ....[From (i)]

`= (- 1)/"2at"^3`

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 3 Differentiation
Miscellaneous Exercise 3 | Q 4.2 | Page 101
Advertisement Remove all ads

Video TutorialsVIEW ALL [2]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×