second derivative of f(x)=square root(x^2+81)

second derivative of f(x)=square root(x^2+81)
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Let y=√(x2+81)=(x2+81)½

dy/dx=½(x2+81)-½(2x)=x/√(x2+81).

Let u=x, then du/dx=1; v=√(x2+81), dv/dx=x/√(x2+81).

d2y/dx2=[v(du/dx)-u(dv/dx)]/v2=(√(x2+81)-x2/√(x2+81))/(x2+81)=

81/(x2+81)3/2 or 81√(x2+81)/(x2+81)2. This is the second derivative.

by Top Rated User (1.2m points)

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