Question

A derivada direcional de f dada por f (x,y)= 4xy na direção do versor u= (1/2) i + (raiz de 3) /(2) j

Answer 1

$D_uf = ( \frac{\partial f}{\partial x } ,\frac{\partial f}{\partial y } ,\frac{\partial f}{\partial z } ) . \frac{\vec u}{|\vec u|} \\\\ D_uf=(4y,4x). \frac{( \frac{1}{2} , \frac{\sqrt{3}}{2} )}{ \sqrt{( \frac{1}{2} )^2+( \frac{\sqrt{3}}{2})^2 } } \\\\ D_uf=(4y,4x). \frac{( \frac{1}{2} , \frac{\sqrt{3}}{2} )}{ \sqrt{ \frac{1}{4} + \frac{3}{4} } } \\\\ D_uf=(4y,4x). \frac{( \frac{1}{2} , \frac{\sqrt{3}}{2} )}{ \sqrt{1} } \\\\ D_uf=(4y,4x). ( \frac{1}{2}, \frac{\sqrt{3}}{2} )$

$D_uf = 4y* \frac{1}{2} + 4x*\frac{\sqrt{3}}{2} \\\\ D_uf = 2y+2x \sqrt{3}$