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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.
Section 1. Logarithms. The mathematics of logarithms and exponentials occurs naturally in many branches of science. It is very important in solving problems related to growth and decay. The growth and decay may be that of a plant or a population, a crystalline structure or money in the bank.
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 ...
Worksheet: Derivatives of the Natural Exponential and Logarithmic Functions. . Compute each derivative using the short-cuts. . 1. d. (ex) = dx. ex. 9. x7 = dx. 2. (xe) = dx. 3. . (5 ex) = dx. d. 4. ( ex) = dx. d. 10. dx. 2 ex 1. = 5 ex + 9. d 1. 5. x. ex + x10 = dx. 6. px. dx. 600ex = d. 11. e2x = dx. d. 12. e x
Logarithmic function and their derivatives. Recall that the function loga x is the inverse function of ax : thus log x. a = y , ay = x: If a = e; the notation ln x is short for log x. e. and the function ln x is called the natural loga-rithm.
1. Introduction. In this unit we look at how we can use logarithms to simplify certain functions before we di er-entiate them. To start o , we remind you about logarithms themselves. If y = ln x, the natural logarithm function, or the log to the base e of x, then. dy 1 =. dx x.
