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Find the second order derivatives of the...

Find the second order derivatives of the functions given.
`x^(20)`

Text Solution

Verified by Experts

Let `y=x^(20)`

Differentiating w.r.t. x

`(dy)/(dx)=(d(x^20))/(dx)`

`(dy)/(dx)=20x^(20-1)`

`(dy)/(dx)=20x^(19)`

Again Differentiating w.r.t. x

`d/dx((dy)/(dx))=(d(20x^(19)))/(dx)`

`(d^2y)/(dx^2)=(20d(x^(19)))/(dx)`

`(d^2y)/(dx^2)=20xx19 x^(19-1)`

`(d^2y)/(dx^2)=20xx19 x^(18)`

`(d^2y)/(dx^2)=380x^(18)`
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