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March 2nd, 2011, 06:26 PM   #1
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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.
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March 2nd, 2011, 07:35 PM   #2
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Re: Derivatives of exponential and log functions review help

1.) I would write f(q) as:



Now, using the product rule, chain rule, and power rule, we have:



Simplify:



Factor:







2.)









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March 3rd, 2011, 10:59 AM   #3
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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??
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March 5th, 2011, 06:23 PM   #4
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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.
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March 6th, 2011, 09:49 AM   #5
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Re: Derivatives of exponential and log functions review help

sorry i mean times q
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