Question

If \(u = e^{xy}\), then the value of \(\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2}\) at (1, 1) is

• A. e
• B. 2e
• C. 1
• D. 0

Hint:

When performing partial differentiation, be methodical. Write down each step clearly to avoid confusion, especially when calculating second-order derivatives. Pay close attention to which variable you are treating as a constant in each step.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
Integrate ∫(log sec x)tan x dx.

Step 2: Key Formula (Alternate):
Substitute t=log sec x, then dt=tan x dx.

Step 3: Detailed Explanation:
Let t=log sec x. dt/dx=tan x → dt=tan x dx. Integral becomes ∫t dt = t²/2 + c = (log sec x)²/2 + c.

Step 4: Final Answer:
Integral is (1/2)(log sec x)² + c.