Question

Find the gradient of the function. Assume the variables are restricted to a domain on which the function is defined. z=2xe2yx+2y. Enter an answer in each field. Enclose numerators and denominators in parentheses. For example, (a−b)/(1+n).

Answer 1

Answer:

$grad(z(x,y))=2[e^{2xy}+2xye^{2xy}]\hat{i}+[4x^{2}e^{2xy}+2]\hat{j}$

Step-by-step explanation:

$z=2xe^{2yx}+2y$

The gradient of a function is

$grad(z(x,y))=D_{x}z(x,y)\hat{i}+D_{y}z(x,y)\hat{j}$

where Dx means derivative over x and the same for Dy. Hence we have

$grad(z(x,y))=2[e^{2xy}+2xye^{2xy}]\hat{i}+[4x^{2}e^{2xy}+2]\hat{j}$

where we have used derivative of a product anf of an exponential function

I hope this is useful for you

regards