Question

Find the partial derivatives indicated Assume the variables are restricted to a domain on which the function is defined. z=x8+3y+xy.

Answer 1

Answer:

Step-by-step explanation:

The question is incomplete. Here is the complete question.

Find the partial derivatives indicated Assume the variables are restricted to a domain on which the function is defined. z=$x^{8}$+$3^{y}$+$x^{y}$

a) Zx b) Zy

In differentiation, if y = axⁿ, y' = $nax^{n-1} \ where \ n\ is\ a\ constant$. Applying this in question;

Given the function z = x⁸+$3^{y}$+$x^{y}$

$Z_x = \frac{\delta z}{\delta x} = 8x^{7} + 0 + yx^{y-1} \\\frac{\delta z}{\delta x} = 8x^{7} + yx^{y-1}$

Note that y is treated as a constant since we are to differentiate only with respect to x.

For Zy;

$Z_y = \frac{\delta z}{\delta y} =0+ 3^{y} ln3 + x^{y}lnx \\\frac{\delta z}{\delta y} = 3^{y} ln3 + x^{y}lnx }$

Here x is treated as a constant and differential of a constant is zero.