"Define g(x,y)=x2+y2−4xy+3y+2" was answered by students like you

cistG

Answered question

2021-09-10

Define $g (x, y) = x^{2} + y^{2} - 4 x y + 3 y + 2$

Answer & Explanation

Tuthornt

Skilled2021-09-11Added 107 answers

Possible derivation:
$\frac{d}{d x} (x^{2} + y^{2} - 4 x y + 3 y + 2)$
Differentiate the sum term by term and factor out constants:
$= \frac{d}{d x} (2) - 4 y (\frac{d}{d x} (x)) + \frac{d}{d x} (x^{2}) + \frac{d}{d x} (3 y) + \frac{d}{d x} (y^{2})$
The derivative of 2 is zero:
$= - 4 y (\frac{d}{d x} (x)) + \frac{d}{d x} (x^{2}) + \frac{d}{d x} (3 y) + \frac{d}{d x} (y^{2}) + 0$
Simplify the expression:
$= - 4 y (\frac{d}{d x} (x)) + \frac{d}{d x} (x^{2}) + \frac{d}{d x} (3 y) + \frac{d}{d x} (y^{2})$
The derivative of x is 1:
$= \frac{d}{d x} (x^{2}) + \frac{d}{d x} (3 y) + \frac{d}{d x} (y^{2}) - 14 y$
Use the power rule, $\frac{d}{d x} (x^{n}) = n x^{n - 1}$ , where n = 2.
$\frac{d}{d x} (x^{2}) = 2 x :$
$= - 4 y + \frac{d}{d x} (3 y) + \frac{d}{d x} (y^{2}) + 2 x$
The derivative of 3 y is zero:
$= 2 x - 4 y + \frac{d}{d x} (y^{2}) + 0$
Simplify the expression:
$= 2 x - 4 y + \frac{d}{d x} (y^{2})$
The derivative of $y^{2}$ is zero:
$= 2 x - 4 y + 0$
Simplify the expression:
$= 2 x - 4 y$
Simplify the expression:
Answer:
$= 2 (x - 2 y)$

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