Grings - Derivada da Função Logarítmica - ( aula 7 )

Quick Course on Derivatives. Derivative of Logarithmic Function. 5 solved exercises. Reviewing: rules of derivation, power, property of logarithm, M.M.C. Subscribe to my CHANNEL to receive FREE classes SITE: http://www.omatematico.com/ Classes on DVD: http://www.lojaomatematico.com.br/ STUDYING has never been so easy! CONTENT: Applying the rule of differentiation: y = ln(x) --- y’ = 1/x in time (1:00) Remembering that ln is a natural or natural logarithm in time (1:16) EXERCISE 1: Determine the derivative of the function: y = 7 ln(x) in time (1:12) NEW TABLE of Derivatives: http://bit.ly/1sQiwOx Using the rule of differentiation 6 EXERCISE 2: Find the derivative of the function: y = ln x³ in time (2:06) Applying the property of the logarithm: log A^p to base c = p log A to base c (where: ^ is read raised to the a) in time (2:45) Video lesson Property of LOGARITHMS: http://bit.ly/211GaSG Property 3 in time (1:40) of this lesson Comment: ln x in base e can be written ---- ln(x) in time (4:01) If the base is ≠ e Example: log x in base 2 in time (4:20) FORMULA used when the base is not e Given the function: y = log x in base a  its derivative is: y’ = 1/x log e in base a in time (4:51) NEW Derivatives TABLE:http://bit.ly/1sQiwOx Using the rule of differentiation 7 Alternative formula: y’ = 1/x ln a in time (5:16) EXERCISE 3: Calculate the derivative of the function: y = 4 log x in base 3 in time (5:46) EXERCISE 4: Calculate the derivative of the function: y = 7 log x + 2 ln x in time (6:59) EXERCISE 5: Calculate the derivative of the function: y = ln (x √x ) in time (9:20) Applying the property of the logarithm: log (AB) to base c = log A to base c + log B to base c in time (9:47) Video lesson on Property of LOGARITHMS: http://bit.ly/211GaSG Property 1 in time (1:40) of this lesson Applying the property: Root that becomes a power: nth root of a^p = a^p/n (where: ^ is read raised to the a) TIP: “whoever is in the shade goes to the sun and whoever is in the sun goes to the shade” in time (10:27) Video lesson on POWERS: http://bit.ly/1TW7OOL property 6 at time (5:49) of this lesson Applying the property of the logarithm: log A^p to base c = p log A to base c (where: ^ is read raised to the a) at time (11:03) Video lesson on Property of LOGARITHMS: http://bit.ly/211GaSG Property 3 at time (1:40) of this lesson Applying the rule of derivation: y = ln(x) --- y’ = 1/x at time (11:36) NEW TABLE of Derivatives:http://bit.ly/1sQiwOx Using the rule of derivation 6 Taking the G.C.M. between x and 2x at time(12:08)