Differen-SAAAAAAY-tion!

Calculus Level 1

Find the sum of the coefficients of f ′ ′ ′ ′ ( x ) f''''(x) in f ( x ) = 3 x 4 + 4 x 3 + 4 x 2 + 6 x + 5 f(x)=3x^4+4x^3+4x^2+6x+5 .


The answer is 72.

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John Paul Bañez Punzalan by John Paul Bañez Punzalan , 22, Philippines

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3 solutions

f '(x) = 12x^3+12x^2+8x+6

f ''(x) = 36x^2+24x+8

f '''(x) = 72x +24

f ''''(x) = 72.

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Luciano Canela
Jan 5, 2015

Knowing the fact the derivative of a constant number is 0, all the last three terms will be 0, before 3*x^4. So, just derivate the first term to find the answer ;)

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f'(x)=12(x^3)+12(x^2)+8^x+6
f"(x)=36(x^2)+24x+8
f"'(x)=72x+24
f""(x)=72 ans=72


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