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KiRa [710]
4 years ago
7

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

+xy.

Mathematics
1 answer:
ahrayia [7]4 years ago
6 0

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.

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