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Find d2ydx2, if y = x5 - Mathematics and Statistics

Sum

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

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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`

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