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February 20th, 2016, 11:55 PM  #1 
Member Joined: Jan 2016 From: Canada Posts: 40 Thanks: 0  Derivatives of Exponential and Log Functions
Hi Guys, I just solved the questions below and need some feedback. Just want to make sure, I solved them correctly. Thank you so much. 1. $\displaystyle y = 0.5e^x3.17e^2x$ Solution: $\displaystyle y' = 0.5e^x(1)  2(3.17)e^2x$ $\displaystyle y' = 0.5e^x6.34e^2x$ ==================================== 2. $\displaystyle 2e^{5x^24x}$ Solution: $\displaystyle g'(x) = 10x4 $ $\displaystyle y' = 2(10x4)e^{5x^24x} $ ========================================== 3. [MATH]y = ln(5x^4x^3)^2[/MATH Solution: $\displaystyle y' = 2(5x^4x^3).(20x^33x^2)/(5x^4x^3)^2$ =========================================== 4. $\displaystyle y=ln\frac {7x1}{12x+5}$ Solution: $\displaystyle g'(x) = \frac{7(12x+5)(7x1)(12)}{(12x+5)^2}$ $\displaystyle = \frac{84x+3584x+12}{(12x+5)^2}$ $\displaystyle = \frac{47}{(12x+5)^2}$ $\displaystyle \frac{g'(x)}{g(x)} = \frac{\frac{47}{(12x+5)^2}}{ \frac{7x1}{12x+5}}$ $\displaystyle = \frac{47(12x+5)}{(12x+5)^2(7x1)}$ 
February 21st, 2016, 12:10 AM  #2 
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics 
1. There's no exponential function in the second term. $\displaystyle 3.17e^2$ is the coefficient of x. 2. I think you're correct, but you may want to factorise the expression in brackets (if your teacher requires it). 3. I think you missed a ln in the first part. In the second part, you should cancel out common factors. 4. Again, you should cancel out the common factors. 
February 21st, 2016, 12:25 AM  #3  
Member Joined: Jan 2016 From: Canada Posts: 40 Thanks: 0  Quote:
$\displaystyle y=0.5e^x−3.17e^{2x}$ $\displaystyle y′=0.5e^x(1)−2(3.17)e^{2x}$ $\displaystyle y′=0.5e^x−6.34e^{2x}$ Is that correct now? By the way, greatly appreciate your quick response. Thank You.  
February 21st, 2016, 12:39 AM  #4  
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics  Quote:
 

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derivatives, exponential, functions, log 
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