Given y=(x2 + 1)3, find dydx and d2ydx2. Show that the second derivative is positive for every real

Question

Given y=(x2 + 1)3, find dydx and d2ydx2. Show that the second derivative is positive for every real input.

Accepted Answer

$\dfrac{\mathrm{d}y}{\mathrm{d}x}=6 x \left(x^{2} + 1\right)^{2}$; $\dfrac{\mathrm{d}^2y}{\mathrm{d}x^2}=6 \left(x^{2} + 1\right) \left(5 x^{2} + 1\right)$ The second derivative is positive for every real $x$.

Second derivatives

Second derivatives

Solution:

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