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Find the directional derivative of the function f(x, y) = x2y7 ? 3y at the point (2, ?1) in the direction of the vector v = 2i + 3j. Solution First we compute the gradient vector at (2, ?1). ?f(x, y) = Correct: Your answer is correct. + (7x2y6 ? 3)j ?f(2, ?1) = ?4i + Incorrect: Your answer is incorrect. Note that v is not a unit vector, but since |v| = Incorrect: Your answer is incorrect. , the unit vector in the direction of v is as follows. u = v |v| = . Therefore, by the equation Duf(x, y) = ?f(x, y) · u, we have the following. Duf(2, ?1) = ?f(2, ?1) · u = ?4i + · + 3 13 j = ?4 · + 25 · 3 13 =Find the directional derivative of the function

`f(x,y)=x^(2)y^(7)-3y`

at the point

`(2,-1)`

in the direction of the vector

`v=2i+3j`

. Solution First we compute the gradient vector at

`(2,-1)`

. Note that

`v`

is not a unit vector, but since

`|v|=`

`u=(v)/(|v|)=`

Therefore, by the equation

`D_(u)f(x,y)=gradf(x,y)*u`

, we have the following. ]