Find second derivative  of function f(x) = \( \rm \frac{(2x^{2} + 3x + 4)}{x}\)

Concept:

\(\rm \frac{\mathrm{d} (x^n)}{\mathrm{d} x} = nx^{n - 1}\)

Calculation:

Given: f(x) = \( \rm \frac{(2x^{2} + 3x + 4)}{x}\)

Differentiation with respect to x

f'(x) = \(\rm \frac{\mathrm{d} \frac{(2x^{2} + 3x + 4)}{x}}{\mathrm{d} x} \)

= \(\rm \frac{\mathrm{d} (2x + 3 + \frac{4}{x})}{\mathrm{d} x}\)

= 2 – 4x^-2

Again; differentiation with respect to x

f'(x) = 0 + 8x^-3

= 8x-3

∴ The required value is  8x-3