Final answer:
To find the first partial derivatives of the function w = u v⁴, differentiate w with respect to u and v separately while treating the other variable as a constant.
Step-by-step explanation:
To find the first partial derivatives of the function w = u v⁴, we will differentiate w with respect to u and v separately while treating the other variable as a constant.
Derivative of w with respect to u: dw/du = 4u v⁴
Derivative of w with respect to v: dw/dv = 4u v³