Find d2ydx2, if y = x5 - Mathematics and Statistics

Sum

Find ("d"^2"y")/"dx"^2, if y = "x"^5

Solution

y = "x"^5

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

"dy"/"dx" = 5"x"^4

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

("d"^2"y")/"dx"^2 = 5 * "d"/"dx" ("x"^4)

= 5(4"x"^3)

∴ ("d"^2"y")/"dx"^2 = 20"x"^3

Concept: Second Order Derivative
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