Question

Find the partial derivatives of the following functions

a) z = 8x^2 − 4xy + 5y^2
b) z = 5xe^y
c) z = 3xln(y)

Answer 1

Hello,

Explanation:

a)

`z=8x^2-4xy+5y^2\\\\(\partial z)/(\partial x) =16x^2-4y\\\\(\partial z)/(\partial y) =-4x+10y\\`

b)

`z=5xe^(y)\\\\(\partial z)/(\partial x) =5e^y\\\\(\partial z)/(\partial y) =5xe^y\\`

c)

`z=3xln(y)\\\\(\partial z)/(\partial x) =3ln(y)\\\\(\partial z)/(\partial y) =(3x)/(y)\\`