If 4x^2+5x+xy=4 and y(4)=−20, find y′(4) by implicit differentiation.

Yair Valentine

Yair Valentine

Open question

2022-08-17

If 4 x 2 + 5 x + x y = 4 and y ( 4 ) = 20, find y ( 4 ) by implicit differentiation.
I implicitly differentiated the equation, but I don't see how I can use y ( 4 ) = 20 to my advantage.

Answer & Explanation

Ben Logan

Ben Logan

Beginner2022-08-18Added 13 answers

From 4 x 2 + 5 x + x y = 4 you get
8 x + 5 + y ( x ) + x y ( x ) = 0.
If x = 4 we have
32 + 5 + y ( 4 ) + 4 y ( 4 ) = 0.
Can you finish now?
sunnypeach12

sunnypeach12

Beginner2022-08-19Added 5 answers

Hint:
8 x + 5 + y ( x ) + x y = 0 y ( x ) = ( y ( x ) + 8 x + 5 ) x

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