Find the directional derivative of f(x, y)=x^2*y+4y^2 at (2, 1) for u=<1/2, sqrt(3)/2>.

Answer: 2+6sqrt(3)

<2xy, 8y> at (2, 1)=<4, 8>

<4, 8>*<1/2, sqrt(3)/2>=2+4sqrt(3)

This doesn't match the answer so can anyone check my work and correct me if I'm wrong? Show your work.

## Comments

x^2*y means (x^2)(y), not x^(2y). And how should I find the derivative to this with respect to y?

You need to treat x as a constant not a variable. For the x

^{2}y you must think of x^{2}as a scalar not a variable. So follow the simple rule of derivatives d/dx[cu] = cu' and you get x^{2}. It is as if you are taking the derivative of a single variable function and you have f(x) = 6x. The derivative in this case would be 6 and just like that case the partial derivative with respect to y is x^{2}+ 8y.