Question

Find d^2y/dx^2 if y/x^2 = 10

A. 0
B. (2y)/x
C. 20
D. y/x
E. (x-2y)/x

Answer 1

Answer:

C. 20

Step-by-step explanation:

$\frac{y}{ {x}^{2} } = 10 \\ \\ y = 10 {x}^{2} \\ \\ differentiating \: w.r.t. \: x \: on \: both \: sides \\ \\ \frac{dy}{dx} = 10 \frac{d}{dx} {x}^{2} \\ \\ \frac{dy}{dx} = 10 \times 2{x} \\ \\ \frac{dy}{dx} = 20{x} \\ \\ differentiating \: again\: w.r.t. \: x \: on \: both \: sides \\ \\ \frac{d}{dx} \bigg(\frac{dy}{dx} \bigg)= 20\frac{d}{dx} {x} \\ \\ \frac{ {d}^{2} y}{d {x}^{2} } = 20 \times 1 \\ \\ \huge \purple {\frac{ {d}^{2} y}{d {x}^{2} } } \red{= } \orange{20}$