Derivative

Calculus Level 1

Given that f ( x ) = 3 x 4 , f(x)=3x^4, find the value of f ′ ( 2 ) . f'(2).


The answer is 96.

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Victor Loh by Victor Loh , 19, Singapore

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3 solutions

Timothy Vu
Aug 22, 2015

f(x) = 3 x 4 3 x^{4} Given equation

f'(x) = ( 3 × 4 ) x 4 − 1 (3 \times 4) x^{4-1} Power Rule

f'(x) = ( 12 ) × ( x 3 ) (12) \times (x^{3}) Simplify

f'(2) = ( 12 ) × ( 2 3 ) (12) \times (2^{3}) Substitution

f'(2) = ( 12 ) × ( 8 ) (12) \times ( 8 ) Simplify

f'(2) = 96 Simplify

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Kenneth Tay
Jul 12, 2014

f ′ ( x ) = 12 x 3 f'(x) = 12x^3 , hence f ′ ( 2 ) = 12 × 8 = 96 f'(2) = 12 \times 8 = 96 .

10 Helpful 0 Interesting 0 Brilliant 0 Confused

how it became 12x^3 it has to be 3x^3=3*16 =>48

Vigneshwar Balasubramanian - 5 years, 7 months ago

Applying the power formula , we get

f ( x ) = 3 x 4 f(x)=3x^4

f ′ ( x ) = 12 x 3 f'(x)=12x^3

f ′ ( 2 ) = 12 ( 2 3 ) = 12 ( 8 ) = f'(2)=12(2^3)=12(8)= 96 \color{#D61F06}\large \boxed{96}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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