Question
The directional derivative of the function f(x, y) = x2 + y2 along a line directed from (0, 0) to (1, 1), evaluated at the point x = 1, y = 1 is
Options :
2
√2
4√2
2√2
Answer :
2√2
Solution :
∇ f = ı̂ (∂f/∂x) + ȷ̂ (∂f /∂y)
∇ f = 2ı̂ + 2ȷ̂
Now, calculating the value of ∇ f in 1ı̂ + 1ȷ̂ D.D of given function is (2ı̂ + 2ȷ̂) x (ı̂ + ȷ̂)/ |ı̂ + ȷ̂| = 2 √2
Copyright © 2025 Test Academy All Rights Reserved