1) f '(x) = ((2x-3)⁵(3x²+2x+1))' = ((2x-3)⁵)'(3x²+2x+1) + (2x-3)⁵(3x²+2x+1)' = 10(2x-3)⁴(3x²+2x+1) + (2x-3)⁵(6x+2) = 2(2x-3)⁴(5(3x²+2x+1)+(2x-3)(3x+1))=2(2x-3)⁴(15x²+10x+5+6x²-7x-3)=2(2x-3)⁴(21x²+3x+2).
f '(1) = 52
2) f '(x) = (⁴√(3x+1)·(3x-14)⁴)' = (⁴√(3x+1))'·(3x-14)⁴+⁴√(3x+1)·((3x-14)⁴)' =
f '(5) =
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Answers & Comments
1) f '(x) = ((2x-3)⁵(3x²+2x+1))' = ((2x-3)⁵)'(3x²+2x+1) + (2x-3)⁵(3x²+2x+1)' = 10(2x-3)⁴(3x²+2x+1) + (2x-3)⁵(6x+2) = 2(2x-3)⁴(5(3x²+2x+1)+(2x-3)(3x+1))=2(2x-3)⁴(15x²+10x+5+6x²-7x-3)=2(2x-3)⁴(21x²+3x+2).
f '(1) = 52
2) f '(x) = (⁴√(3x+1)·(3x-14)⁴)' = (⁴√(3x+1))'·(3x-14)⁴+⁴√(3x+1)·((3x-14)⁴)' =
f '(5) =