Saved Bookmarks
| 1. |
If y = ekx then \(\rm \frac {d^2 y}{dx^2}\) =1. y2. ky3. k2y4. ekx |
|
Answer» Correct Answer - Option 3 : k2y Concept: Second-order Derivative. \(\rm \frac {d^2 f(x)}{dx^2} = \) \(\rm \frac {d}{dx} [\frac {d}{dx} f(x)]\) \(\rm \frac {d}{dx}e^{f(x)} = e^{f(x)} f'(x)\)
Calculations: Let y = ekx Differentiating w.r. to x on both side, we get ⇒\(\rm \dfrac {dy}{dx} = ke^{kx}\) Again Differentiating w.r. to x on both sides, we get ⇒\(\rm \dfrac {d^2y}{{dx}^2} = k^2e^{kx}\) ⇒\(\rm \dfrac {d^2y}{{dx}^2} = k^2y\) Hence, If y = ekx then \(\rm \dfrac {d^2y}{{dx}^2} = k^2y\) |
|