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Logarithmic Differentiation Date_____ Period____ Use logarithmic differentiation to differentiate each function with respect to x. 1) y = 2x2 x dy dx = y(2ln x + 2) = 4x2x(ln x + 1) 2) y = 5x5x dy dx = y(5ln x + 5) = 25 x5x(ln x + 1) 3) y = 3x3x dy dx = y(3ln x + 3) = 9x3x(ln x + 1) 4) y = 4xx 4 dy dx = y(4x3 ln x + x3) = 4xx 4 + 3 (4ln x + 1 ...
Worksheet on Logarithmic Differentiation (Solutions) Math 1a: Introduction to Calculus 21 March 2005 For each of the following, differentiate the function first using any rule you want, then using logarithmic differentiation: 1. y = x2 Solution. If y = x2, then lny = ln(x2) = 2lnx. Differentiating, 1 y dy dx = 2 x, so dy dx = 2y x = 2x2 x ...
This technique, called ‘logarithmic differentiation’ is achieved with a knowledge of. (i) the laws of logarithms, (ii) the differential coef-ficients of logarithmic functions, and (iii) the differ-entiation of implicit functions.
Differentiation - Natural Logs and Exponentials. Differentiate each function with respect to x. 1) y = ln x3. 3) y = ln ln 2 x4. 5) y = cos ln 4 x3. ( 4 x3 + 5)2. 7) y = e. 4 x4. 9) y = ln ( − x3 − 3 )5.
Differentiation - Logs and Exponentials. Differentiate each function with respect to x. 1) y = 44 x4. 3) y = log 3 x2. 3. 5) y = log ( 3 x5 + 5)5. 3. x3. 7) y = ( 4 + 2)3.
Differentiation by taking logarithms. In this unit we look at how we can use logarithms to simplify certain functions before we differ-entiate them. In order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that they become second nature.
Worksheet on Logarithmic Differentiation Math 1a: Introduction to Calculus 21 March 2005 For each of the following, differentiate the function first using any rule you want, then using logarithmic differentiation: 1. y = x2 2. y = ex 3. y = √ x2 +1 4. y = xsinx 5. y = x x2+2 6. y = p (x2 +1)(x−1)2.
