Question:
If y = ex2 sin 2x, then what is (dy)/(dx) at x = π equal to?
If y = ex2 sin 2x, then what is (dy)/(dx) at x = π equal to?
Options:
- 2eπ2
- 2πeπ2
- (1 + π)eπ2
- eπ2
- 2eπ2
- 2πeπ2
- (1 + π)eπ2
- eπ2
Correct Answer: a)
Explanation:
We have, y = ex2 sin 2x
On differentiating both sides w.r.t. x, we get:
dy/dx = 2 cos(2x) ex2 + 2x ex2 sin(2x)
At x = π:
dy/dx = 2 cos(2π) eπ2 + 2π eπ2 sin(2π)
= 2 (1) eπ2 + 2π eπ2 (0) = 2eπ2 (Option a)
We have, y = ex2 sin 2x
On differentiating both sides w.r.t. x, we get:
dy/dx = 2 cos(2x) ex2 + 2x ex2 sin(2x)
At x = π:
dy/dx = 2 cos(2π) eπ2 + 2π eπ2 sin(2π)
= 2 (1) eπ2 + 2π eπ2 (0) = 2eπ2 (Option a)