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Calculus Level 2

Let f ( x ) = x 3 ln ⁡ x f(x) = x^3 \ln x .

Find f ′ ( 3 ) f'(3) to two decimal places.


The answer is 38.66.

Denton Young by Denton Young , 47, USA

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1 solution

Denton Young
Sep 6, 2016

By product rule, f ′ ( x ) = ( ( ( x 3 ) ′ × ( l n x ) ) + ( ( x 3 ) × ( l n x ) ′ ) ) f'(x) = (((x^3)' \times (ln x)) + ((x^3) \times (ln x)'))

This becomes ( ( 3 x 2 × ( l n x ) ) + x 2 ) ((3x^2 \times (ln x)) + x^2)

Substitute x = 3 and you get 27 l n 3 + 9 27 ln 3 + 9 = 38.66

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