log-diff-sol

log-diff-sol - Logarithmic Differentiation Worksheet To...

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Unformatted text preview: Logarithmic Differentiation Worksheet To find the derivative of f (x) = (x2 + 3)100 xx (5x2 - 2)3 2 (x2 + 3)100 xx , we do the following steps. (5x2 - 2)3 2 f (x) = ln f (x) = ln (x2 + 3)100 xx (5x2 - 2)3 2 2 Take the natural log of both sides Simplify using rules of logs Take the derivative of both sides Compute the derivatives Solve for Dx (f (x)) and simplify. ln f (x) = 100 ln(x2 + 3) + x2 ln x - 3 ln(5x2 - 2) Dx (ln f (x)) = Dx (100 ln(x + 3) + x ln x - 3 ln(5x - 2)) 1 100(2x) x2 3(10x) Dx (f (x)) = 2 + 2x ln x + - 2 f (x) x +3 x 5x - 2 200x 30x + (2x ln x + x) - 2 Dx (f (x)) = f (x) 2+3 x 5x - 2 2 2 Find derivatives of the following functions, using logarithmic differentiation. The solutions are not simplified completely so that you can understand them better. 1. xx (xx ) (1 + ln x) 2. xx 2 +3x xx 2 +3x x2 + 3x + (ln x) (2x + 3) x 3. x x x x x ln x + x 2 x - ln x 1 + 2 2 x x 4. xx -1 xx -1 5. xln x xln x 2 ln x x ex ln x + ex x (2x + 5) (ln (ln x)) + x2 + 5x x ln x 6. xe x xe x 7. (ln x)x 2 +5x (ln x)x 2 +5x 8. (f (x))g(x) (f (x))g(x) g (x) ln f (x) + g (x) f (x) f (x) 1 9. (6x3 - 3) (x - 2)9 (4x + 3x)2 (x2 + 4) (4x + 3x)2 10. (6x3 - 3)4 8 4 8 8 4 6x3 - 3 4 (x - 2)9 (4x + 3x)2 4 (18x2 ) 9 27 + + 3-3 6x x-2 7x (x2 + 4) (4x + 3x)2 (6x3 - 3)4 8 (2x) 2 7 4 (18x2 ) + - 3 x2 + 4 7x 6x - 3 11. (x2 + 4) (6x3 - 3) (4x + 3x)2 (x - 2)9 (x2 + 4) (6x3 - 3) (4x + 3x)2 (x - 2)9 8 4 9 8 (2x) 4 (18x2 ) 2 7 + 3 + - 2+4 x 6x - 3 7x x-2 2 ...
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log-diff-sol - Logarithmic Differentiation Worksheet To...

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