Find the gradient of the curve xlny−x/y=2 at (−1,1)

Dorsheele0p

Dorsheele0p

Open question

2022-08-13

Find the gradient of the curve x ln y x y = 2 at (−1,1)
I've done something wrong as I got the gradient to be 0 when the answer in the back says −0.5
Can someone help me with this question?
edit:
I got: 1 + 1 y d y d x y x d y d x y 2
y 2 + y d y d x y x d y d x = 0
d y d x = y y 2 y x
Substituting the values in did not get me the answer

Answer & Explanation

wietselau

wietselau

Beginner2022-08-14Added 28 answers

When you differentiate you get:
ln y + x y y y x y y 2 = 0
Then substituting x = 1 , y = 1 you obtain: y ( 1 + y ) = 0 so y = 1 / 2.

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