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 

Advertisement Remove all ads
Share
Notifications

View all notifications

Forgot password?