Question

Which expression defines the second order derivative of \[y\] with respect to \[x\]?

Options

• \[\frac{d^2y}{dx^2}=\frac{d}{dx}\left(\frac{dy}{dx}\right)\]

• \[\frac{d^2y}{dx^2}=\frac{dy}{dx}\]

• \[\frac{d^2y}{dx^2}=\frac{d}{dx}(y)\]

• \[\frac{d^2y}{dx^2}=\frac{d}{dy}\left(\frac{dx}{dy}\right)\]

Answer 1

The second order derivative is found by differentiating the first derivative \[\frac{dy}{dx}\] with respect to \[x\]. Hence its defining expression is \[\frac{d}{dx}\left(\frac{dy}{dx}\right)\].