F(y) = 1 y2 − 7 y4 (y + 3y3)

Answer 1

F(y) = 1y² -7y⁴ (y+3y³)

(Let me know if I didn't write the function correctly)

Derive the first term with exponent rule and the second term with product rule:

dF/dy = 2y - [(7y⁴)(1+9y²)+(28y³)(y+3y³)]

Perform multiplication:

dF/dy = 2y - 7y⁴-63y⁶-28y⁴- 84y⁶

Combine like terms:

dF/dy = 2y - 35y⁴-147y⁶