Find the Gradient Vector Field of the Scalar Function $f$ (That Is, Find the Conservative Vector Field

question 83

Short Answer

Find the gradient vector field of the scalar function $f$ . (That is, find the conservative vector field $\mathbf { F }$ for the potential function $f$ of $\mathbf { F }$ .)
$$f ( x , y , z ) = 6 x y ^ { 3 } + 8 y z ^ { 4 }$$

---

Definitions:

Positive Exponents

Exponents that are greater than zero, indicating the number of times the base is multiplied by itself.

Expression

A combination of symbols that represents a quantity or mathematical relation, including numbers, operation symbols, and sometimes variables.

Rules Of Exponents

Fundamental principles used to simplify expressions involving powers of the same base, including multiplication, division, and power of power rules.

Expression

A combination of symbols that represents a quantity or a relationship between quantities.