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=[tex]x^{8}[/tex]+[tex]3^{y}[/tex]+[tex]x^{y}[/tex]
a) Zx b) Zy
In differentiation, if y = axⁿ, y' = [tex]nax^{n-1} \ where \ n\ is\ a\ constant[/tex]. Applying this in question;
Given the function z = x⁸+[tex]3^{y}[/tex]+[tex]x^{y}[/tex]
[tex]Z_x = \frac{\delta z}{\delta x} = 8x^{7} + 0 + yx^{y-1} \\\frac{\delta z}{\delta x} = 8x^{7} + yx^{y-1} \\[/tex]
Note that y is treated as a constant since we are to differentiate only with respect to x.
For Zy;
[tex]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 } \\[/tex]
Here x is treated as a constant and differential of a constant is zero.
