Question

Find the second order derivatives of the function. logx

Answer 1

we know, if any function y = logf(x) is given
then, dy/dx = $\frac{f'(x)}{f(x)}$
[ note :- here f'(x) denotes 1st derivatives of f(x).]

Given, y = logx
now, differentiate y with respect to x
$\frac{dy}{dx} = \frac{1}{x}\frac{dx}{dx}$
hence, dy/dx = 1/x

for getting 2nd order derivatives, differentiate dy/dx once again.
e.g., d²y/dx² = d(1/x)/dx = d(x⁻¹)
= -x⁽⁻¹⁻¹⁾ = -x⁻² = -1/x²

hence, 2nd order derivatives of function is d²y/dx² = -1/x²

Answer 2

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