Differentiate
-f(x) = (-3 $x ^ { 7 }$ - $x ^ { 4 }$ )(2 $x ^ { 2 }$ - 5x + 3)
A) -84 $x ^ { 7 }$ - 105 $x ^ { 6 }$ + 16 $x ^ { 4 }$ + 20 $x ^ { 3 }$
B) -84 $x ^ { 7 }$ + 105 $x ^ { 6 }$ - 16 $x ^ { 4 }$ + 20 $x ^ { 3 }$
C) -54 $x ^ { 8 }$ + 120 $x ^ { 7 }$ - 63 $x ^ { 6 }$ - 12 $x ^ { 5 }$ + 25 $x ^ { 4 }$ - 12 $x ^ { 3 }$
D) 30 $x ^ { 8 }$ - 90 $x ^ { 7 }$ + 63 $x ^ { 6 }$ + 4 $x ^ { 5 }$ - 15 $x ^ { 4 }$ + 12 $x ^ { 3 }$

Question

Quizplus · Accepted Answer

To differentiate the product of two functions, use the product rule: (u*v)' = u'v + uv'. Here, u = -3x^7 - x^4 and v = 2x^2 - 5x + 3. Differentiate each: u' = -21x^6 - 4x^3, v' = 4x - 5. Apply the product rule and simplify to get the correct polynomial.

Differentiate -F(x) = (-3 x7x ^ { 7 }x7 - x4x ^ { 4 }x4

Differentiate
-F(x) = (-3 $x ^ { 7 }$ - $x ^ { 4 }$