Question

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

• A. True
• B. False

Answer 1

The correct option is B False

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 $\frac{dy}{dx}\times \frac{dy}{dx}$ So the above statement is false.