Maths
posted by Karoline .
Differentiate y=(5x2)^3(3x)^6 using the product rule.
i don't get the step where they find the common factor could you help me by doing it step by step please ?
thank you!

Maths 
drwls
There is no such step that i have ever heard of.
Let
u (x) = (5x2)^3 and
v (x) = (3x)^6
You want the derivative of u*v with respect to x.
dy/dx = d(uv)/dx = u dv/dx + v du/dx
That is the product rule.
Now all you have to calculate is du/dx and dv/dx, multiply the v and u terms and add the result. 
Maths 
Karoline
thanks!
there is an example here and where i get lost is a step where it goes from
dy/dx = d(uv)/dx = u dv/dx + v du/dx
= (5x2)^3[6(3x)^5]+(3x)^6[15(5x2)^2]
= (5x2)^2(3x)^5(30x+12+4515x)
is there a step between there that you could show me how to do so i can understand it ?
thank you! 
Maths 
Reiny
You must be talking about the simplication after you found the derivative.
look at the line ....
(5x2)^3[6(3x)^5]+(3x)^6[15(5x2)^2]
= 6(5x2)^3(3x)^5 + 15(3x)^6(5x2)^2
now I see the following common factors
3 for the constants
(5x2)^2 and
(3x)^5
so
= 3(5x2)^2(3x)^5[2(5x2)  5(3x)]
= 3(5x2)^2(3x)^5[10x  4  15 + 5x]
= 3(5x2)^2(3x)^5(15x  19)
Your last line is not fully factored. 
Maths 
Karoline
ah OK, now i get it.
Thank you so much!! 
Maths 
Karoline
hey sorry, one more thing.
How do you find 3
as in
now I see the following common factors
3
how ? 
Maths 
MathMate
(30x+12+4515x)
=3(15x19)
Respond to this Question
Similar Questions

math,help
Can someone show me how step by step how to solve this problem... Rewrite the middle term as the sum of two terms and then factor by grouping. x^22x63 step 1. Find two factors which when multiplied will give you 63 and when added … 
Algebra help
f(x)=x^34x^2x+4 How do I find the xintercept for this? 
algebra
what is the factor by removing the greatest common factor for x126x5, step by step 
ALGEBRA HELP
When solving the equation, what property was used to go from step 3 to step 4? 
Quick math help
In which step below does a mistake first appear in simplifying the expression? 
Algebra 1StepbyStep
Can someone show me how to solve these stepbystep? 
Calc
Differentiate f and find its domain. Show step by step please! f(x)=lnlnln(x) Thanks! 
Math (Calculus)
Hello, Could somebody please help me with the following question? 
Physics
An arrow is shot straight up from the edge of a cliff with an initial velocity of 50 ft/s. Answer the following questions using English units. The acceleration due to gravity has a magnitude of 32.2 ft/s. A. Find the time to reach … 
aps
There are 26 step on flpor at the time saad comes down two step imad step up one step When will tyey meet at what step?