Question

Consider the following equation f (x,y) = x2y. Find the derivative of f
in the direction of (1, 2) at the point (3, 2) is​

Answer 1

Answer my question first then I will answer yours I will

Answer 2

Given:-

Consider the following equation $f(x,y)=x^{2} y$.

To Find:-

Find the derivative of f (x, y) in the direction of (1, 2) at the point (3, 2) is​

Solution:-

here, it is given that -

$f(x,y)=x^{2} y$.

therefore,

$f_{x}=2xy \\\\f_{y}=x^{2}$  

 where $f_{x}$  and $f_{y}$ is the derivative of f(x, y) with respect to x and y respectively.

Now, we have to find the derivative of f(x, y) in the direction of (1,2)

therefore,

$u=1i+2j$

implies, direction derivative of f(x, y) in the direction of (1,2) is given as

$D_{u}=f_{x}(1)+f_{y}(2)\\\\ = 2xy+2x^{2}$

Now ,

$D_{u}(3,2)=2*(3)(2)+2*(3)^{2}\\\\ = 12+18\\\\ =30$

Hence, derivative  of f(x, y) in the direction of (1,2) at the point (3,2) is 30.