Question

If $y=f\left(x\right),then\frac{d^{2}y}{d{x}^2}=$

• A. ${\frac{\left(dy\right)}{dx}}^2$
• B. $\frac{dy}{{dx}^2}$
• C. $\frac{dy}{dx}\times \frac{dy}{dx}$
• D. $\frac{d\left(\frac{dy}{dx}\right)}{dx}$

Answer 1

The correct option is D $\frac{d\left(\frac{dy}{dx}\right)}{dx}$

As discussed in the videos that for a function $y=f\left(x\right),\frac{d^{2}y}{d{x}^2}isnot\left(\frac{dy}{dx}\right)$ multiplied twice. Rather $\frac{d^{2}y}{d{x}^2}$ is the second order derivative of derivative of f(x) or mathematically you can write it as:

$\frac{d^{2}y}{d{x}^2}=\frac{d}{dx}\left(\frac{dy}{dx}\right)$ which is obviously different from $\frac{dy}{dx}\times \frac{dy}{dx}$