Answer to Question #93983 in Calculus for Abdoul

Question

Given\\ (f(x)=3x(x-1)^{5} compute \\ (f\`\`\`(x)\\)

Answer 1

$f(x)=3x(x-1)^5$

$f'(x)=3(x-1)^5+3x\cdot 5(x-1)^4=$

$=3(x-1)^4(x-1+5x)=3(x-1)^4(6x-1)$

$f''(x)=3\cdot 4(x-1)^3(6x-1)+3(x-1)^4\cdot 6=$

$=6(x-1)^3(12x-2+3x-3)=30(x-1)^3(3x-1)$

$f'''(x)=30\cdot 3(x-1)^2(3x-1)+30(x-1)^3\cdot 3=$

$=90(x-1)^2(3x-1+x-1)=180(x-1)^2(2x-1)$

Answer: $f'''(x)=180(x-1)^2(2x-1)$