Question #320377

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


1
Expert's answer
2022-03-30T08:46:43-0400

f(x)=(3x+1)4(2x1)5f(x)=(3x+1)⁴(2x-1)⁵


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


v=(2x1)5=>dvdx=10(2x1)4v=(2x-1)⁵=>\frac{dv}{dx}=10(2x-1)⁴


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


f(x)=(2x1)512(3x+1)3+(3x+1)410(2x1)4f'(x)=(2x-1)⁵•12(3x+1)³+(3x+1)⁴•10(2x-1)⁴


f(x)=2(2x1)4(3x+1)3[6(2x1)+5(3x+1)]f'(x)=2(2x-1)⁴(3x+1)³[6(2x-1)+5(3x+1)]


f(x)=2(2x1)4(3x+1)3[12x6+15x+5]f'(x)=2(2x-1)⁴(3x+1)³[12x-6+15x+5]


f(x)=2(2x1)4(3x+1)3[27x1]f'(x)=2(2x-1)⁴(3x+1)³[27x-1]




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