Calculus
posted by Corin .
How would I go about finding the derivative of f(x)=ln(x)(7x2)^3
first=ln(x)
second= (7x2)^3
Would I do first times the derivative of the second + second times the derivative of the first?
If so, what is the derivative of lnx?
I'm confused.
Thanks for your help.
Cori

"Would I do first times the derivative of the second + second times the derivative of the first?"
That's right. But whenever you are not sure about such a rule you should derive it yourself from first principles. Otherwise you are just going to use a rule that you don't understand.
The derivative of ln(x) is 1/x. 
f(x)=lnx
f'(x)= 1/x
If I remember correctly your going to have to derize the second one again
(chain rule)
(7x2)^3
x= 7x2
dx= 7
(x)^3dx get the derivative of this
3(x)^31 dx + c
3(x)^2 dx + c
and plugging in the found values...
3(7x2)^2 ( 7)= 21(7x2)^2
(2nd part)
For the first part
it Should just be ln(x)= 1/x if I'm not incorrect (my text uses 2 functions instead of using ln so I'm not 100% sure)
so putting it together assuming my thinking is correct:
(1/x )(21(7x2)^2)
since the 2nd was already differentiated..
by the product rule if I remember correctly
f'(x)= (1/x)+(21(7x2)^2) 
I forgot a important part..the first part is to use the product rule
derivative of the first * second function + first*derivative of the second
then doing this again,correcting that error
f(x)= ln(x)(7x2)^3
product rule first then the chain rule for (7x2)^3
(1/x)(7x2)^3 + (lnx)3(7x2)^2
chain rule for the 2nd part
x = 7x2
dx = 7
~you could replace the internal equation 7x2 with x or not but
if you do
(1/x)(7x2)^3 + (lnx)3(x)^2dx
plug in the values of x and dx and
(1/x)(7x2)^3 + (lnx)3(7x2)^2(7)=
(1/x)(7x2)^3 + 21 (lnx)(7x2)^2
(I didn't go and simplify though) 
Thanks so much for all your help. I figured it out.
Cori
Respond to this Question
Similar Questions

Calculus
R=M^2(c/2m/3) dR/dM=CMM^2 I found the derivative. Now how would I find the vale of M that maximize the derivative dR/dM? 
College Calculus 1
We have to find the first and second derivative of f(x)=x^(2/3)(6x)^(1/3) I have the first derivative as being (4x)/(x^(1/3)(6x)^(2/3)) And that I know is right. The second derivative is 8/(x^(4/3)(6x)^(5/3)) I did all the work … 
calculus
Please help with this. I need the first derivative of f(x)=4(x+squareroot (x(8x)) and then the second derivative of this to show by the second derivative test that it is a local maximum. This is difficult to put into form here and … 
calculus
Please help with this. I submitted it below and was asked to clarify by Henry (hope this is clearer and thank you). I need the first derivative of f(x)=4(x+ sqrt (x(8x)).And then the second derivative of this to show by the second … 
calculus
Find the first and second derivative  simplify your answer. y=x/4x+1 I solved the first derivative and got 1/(4x+1)^2 Not sure if I did the first derivative right and not sure how to do the second derivative. 
Calculus
I need help with finding first and second derivativesimplify your answer. Y=xtan(x) I solved first derivative xsec^2(x) + tan(x) I don't understand how to get the first...can someone show me the steps with explanation? 
Calculus
I need to find the second derivative of y=x(x1)^1/2. I found the first derivative is 2x1/2(x1)^1/2, if someone could check, but I am miserably stuck on the second derivative. 
Applied Calculus
Find the first and second derivative of the function: x/(7x+10) Using quotient rule. This is part of my homework in the section named "Higher Order Derivatives". I am confused on getting the second derivative, as I found the first … 
CALC 1
Suppose that h is a function with h'(x) = xe^x. Find all intervals where the function h is concave up. Now, I understand that concavity is determined by the second derivative, so what my question here is, is it just taking the first … 
math
For what intervals is g(x) = 1/x2 + 1 concave down?