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Day03-1432class

# Day03-1432class - 2 3 x dx 2x 1-âˆ 2 3 5 x dx 2x 1-âˆ 2 3 d...

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Math 1432 Section 23986 Pam Balthazar [email protected] 620 PGH Office Hours in 222 Garrison (CASA): Starting Wednesday Monday 1 – 3:30 p.m. Wednesday 1 – 3:30 p.m. Friday 1 – 2 p.m.

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Homepage www.math.uh.edu/~pamb and click on Calculus 1432 Reminder: Homework 1 is due Monday in lab. Homework 2 will due Friday (9/10). Take the online quizzes.
7.2/7.3 Quick Review. . . Expand: ( 29 3 4 2 x 2 x x 4 ln + + Combine into a single logarithm. ( 29 ( 29 2 4 1 x 2 x 1 2 x 2 ln ln ln - + - -

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Solve for x. 5 5 5 3 x 2 2 2 4 log log log - = Solve for x. ( 29 ( 29 2 2 x 2 x 1 2 log log + - - =
Solve for x. ( 29 4 4 x x 12 3 log log + - = Review… Definition of the Natural Logarithm Function x 1 1 x dt x 0 t ln = d 1 x x 0 dx x ln = d u u dx u ' ln = u a positive function of x

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Find the derivatives. ( 29 ( 29 3 x x 5 f ln = + ( 29 x x 1 x f ln = + ( 29 ( 29 z 2x 19x ln ln =
( 29 y x ln ln = ( 29 2 y 1 x ln = + ( 29 2 y x sin ln =

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( 29 ( 29 + = + + 4 4 2 x 3 y x 12 x 5 Surely, not…. Use logarithmic differentiation.
Remember….. dx x C x 0 x ln , = + ( 29 ( 29 ( 29 ( 29 g x g x C g x 0 g x ' ln , = + Examples: 2 1 x 3x dx x + + 2 3 18x 5 dx 5x 6x - -

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2 3 x dx 2x 1 - 2 3 5 x dx 2x 1 -

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Unformatted text preview: 2 3 x dx 2x 1-âˆ« 2 3 5 x dx 2x 1-âˆ« 2 3 d 3 sec tan Î¸ Î¸ Î¸ âˆ« 2 t dt 2 t csc cot = + âˆ« You already know theseâ€¦. . Right??? Now, learn these. d tan Î¸ Î¸ âˆ« d cos sin = âˆ« Î¸ sec = âˆ« t dt sec = âˆ« t dt 2 x x dx x 1 ec tan sec s =-âˆ« csc = âˆ« 2x dx Section 7.4 The Exponential Function So, the easiest derivative there isâ€¦. ( 29 x x e f = ( 29 x f ' = x d e dx = Sometimes it is easier to write exp (x) instead of e x Thus , u is a function of x And, ( 29 ( 29 x x d d x e x e dx dx exp exp = = = ( 29 ( 29 u u d du u u dx dx d du e e dx dx exp exp = = x x e dx e C = + âˆ« u u e du e C = + âˆ« Examples: 2 x x d e dx sin + 2 x 1 d e dx-2 x d e dx-d 3 dx x exp- x x e e y 2 y ln '-+ = = 2 x e dx âˆ« x xe dx cos sin âˆ« 4 3 x x e dx-âˆ«...
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Day03-1432class - 2 3 x dx 2x 1-âˆ 2 3 5 x dx 2x 1-âˆ 2 3 d...

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