For f(x,y) = x²y + 3y, evaluate the partial derivative fx at the point (2, 5).

Practice question · Numerical answer

For $f(x,y) = x^{2}y + 3y$ , evaluate the partial derivative $f_x$ at the point $(2, 5)$ .

Hints

Treat $y$ as a constant and differentiate in $x$ : the $3y$ term dies.
$f_x = 2xy$ ; substitute $x = 2, y = 5$ .

Show the answer

20 (answers within ±0.01 count)

Why

$f_x = 2xy = 20$ . Note how the $3y$ term, constant as far as $x$ is concerned, vanished entirely: partial differentiation sees only the variable it interrogates.

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For f(x,y)=x2y+3yf(x,y) = x^{2}y + 3yf(x,y)=x2y+3y, evaluate the partial derivative fxf_xfx​ at the point (2,5)(2, 5)(2,5).

Practise Partial Derivatives

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For $f(x,y) = x^{2}y + 3y$ , evaluate the partial derivative $f_x$ at the point $(2, 5)$ .