AP EAMCET2011MathematicsDifferentiation
If y= _e x x and z= _e x , then d^2 y d z^2 + d y d z is equal to
Options
- Ae^ -z
- B2 e^ -z
- Cz e^ -z
- D-e^ -z
Correct answer
D. -e^ -z
Step-by-step solution
Given, y= _e x x and z= _e x y= z e^z On differentiating w.r.t. z , we get d y d z = e^z(1)-z e^z e^ 2 z = 1-z e^z Again differentiating, we get aligned d^2 y d z^2 & = e^z(-1)-(1-z) e^z e^ 2 z & = -2+z e^z aligned d^2 y d z^2 + d y d z = 1-z e^z + -2+z e^z =- 1 e^z =-e^ -z