My Math Forum Derivatives of exponential and log functions review help!

 Calculus Calculus Math Forum

 March 2nd, 2011, 06:26 PM #1 Senior Member   Joined: Feb 2011 Posts: 118 Thanks: 0 Derivatives of exponential and log functions review help! Hi, I've got a few questions that I need help on. 1) Find the derivative of the following function: f(x)= (880/q)+4300*(e^((3q+6)/(830))/q) 2) Find y' if y=(9x+10)^4x+6 (I know it's got to do with taking the natural logarithm of both sides, but I don't know how to actually do show it.) ln y= ln________________ b) Simplify by using properties of logarithms: ln y=________________ c) Differentiate both sides with respect to x: y'/y=__________________ d) Solve for y': y'=y*(__________________________) e) Substitute the original expression y to get y' in terms of x only: y'=____________________. I would appreciate some solutions to the following problems, Thank you.
 March 2nd, 2011, 07:35 PM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Derivatives of exponential and log functions review help 1.) I would write f(q) as: $f(q)=20q^{-1}$$44+215e^{\frac{3}{830}(q+2)}$$$ Now, using the product rule, chain rule, and power rule, we have: $f'(q)=$$20q^{-1}$$$$215e^{\frac{3}{830}(q+2)}\frac{3}{830}$$+$$-20q^{-2}$$$$44+215e^{\frac{3}{830}(q+2)}$$$ Simplify: $f'(q)=$$20q^{-1}$$$$\frac{129}{166}e^{\frac{3}{830}(q+2)}$$-$$20q^{-2}$$$$44+215e^{\frac{3}{830}(q+2)}$$$ Factor: $f'(q)=20q^{-2}$$\frac{129q}{166}e^{\frac{3}{830}(q+2)}-\(44+215e^{\frac{3}{830}(q+2)}$$\)$ $f'(q)=20q^{-2}$$\frac{43\(3q-830$$}{166}e^{\frac{3}{830}(q+2)}-44\)$ $f'(q)=\frac{10}{83q^2}$$43\(3q-830$$e^{\frac{3}{830}(q+2)}-7304\)$ 2.) $y=$$9x+10$$^{4x+6}$ $\ln y=\ln$$\(9x+10$$^{4x+6}\)$ $\ln y=$$4x+6$$\ln$$9x+10$$$ $\frac{y'}{y}=$$4x+6$$\frac{9}{9x+10}+4\ln$$9x+ 10$$$ $y'=y$$\frac{18\(2x+3$$}{9x+10}+4\ln$$9x+10$$ \)$ $y'=$$9x+10$$^{4x+6}$$\frac{18\(2x+3$$}{9x+10}+ 4\ln$$9x+10$$\)$
 March 3rd, 2011, 10:59 AM #3 Senior Member   Joined: Feb 2011 Posts: 118 Thanks: 0 Re: Derivatives of exponential and log functions review help One more question for part 1. If i were to find the marginal cost of the derivative of the function. What would the answer be if q=103??
 March 5th, 2011, 06:23 PM #4 Newbie   Joined: Feb 2011 Posts: 21 Thanks: 0 Re: Derivatives of exponential and log functions review help The TA was wrong, if u wanna solve the first one u have to divide the average marginal cost formula by q then take the derivative. I tried his way but it doesnt work.
 March 6th, 2011, 09:49 AM #5 Newbie   Joined: Feb 2011 Posts: 21 Thanks: 0 Re: Derivatives of exponential and log functions review help sorry i mean times q

 Tags derivatives, exponential, functions, log, review

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post li1995717 Calculus 2 October 24th, 2013 02:19 AM pomazebog Calculus 2 March 5th, 2012 08:23 AM ProJO Calculus 4 March 13th, 2011 06:49 PM lilxswttooth Calculus 1 September 21st, 2009 04:50 AM ClipsClips99 Calculus 2 May 21st, 2007 01:57 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top