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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. 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.
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 ...
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.
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.
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.
d 1. (loge x) = . dx x. We can use these results and the rules that we have learnt already to differentiate functions which involve exponentials or logarithms. Example. Differentiate log. e (x2 + 3x + 1). Solution. We solve this by using the chain rule and our knowledge of the derivative of log x. e. d d. loge (x2 + 3x + 1) = (loge u) dx dx.
