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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 ...
- Differentiation - Natural Logs and Exponentials Date Period - Kuta Software
Differentiation - Natural Logs and Exponentials....
- Differentiation - Logs and Exponentials Date Period - Kuta Software
Differentiation - Logs and Exponentials. Differentiate each...
- Differentiation - Natural Logs and Exponentials Date Period - Kuta Software
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 ...
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.
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 - 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.
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.
LOGARITHMIC DIFFERENTIATION As we learn to differentiate all the old families of functions that we knew from algebra, trigonometry and precalculus, we run into two basic rules. The first is for polynomials. When taking the derivative of a polynomial, we use the power rule (both basic and with chain rule): d dx xn = nxn - 1 d dx
