Answer to Question #320377 in Calculus for koi

Question

Differentiate the function 𝑓(𝑥) = (3𝑥 + 1) 4 (2𝑥 − 1) 5 and simplify your answer

Answer 1

$f(x)=(3x+1)⁴(2x-1)⁵$

Let $u=(3x+1)⁴ =>\frac{du}{dx}=12(3x+1)³$

$v=(2x-1)⁵=>\frac{dv}{dx}=10(2x-1)⁴$

$f'(x)=v\frac{du}{dx}+u\frac{dv}{dx}$

$f'(x)=(2x-1)⁵•12(3x+1)³+(3x+1)⁴•10(2x-1)⁴$

$f'(x)=2(2x-1)⁴(3x+1)³[6(2x-1)+5(3x+1)]$

$f'(x)=2(2x-1)⁴(3x+1)³[12x-6+15x+5]$

$f'(x)=2(2x-1)⁴(3x+1)³[27x-1]$