A differentiating the function question.?

Question

Hi I would like to find out the answer to this question.

I would like to

Differentiate the function p(x) with respect to x, given that

p(x) = ( x+4 ) ^6 ( x+7 )^ 2

what does p'(x) =

Thanks for any help received it is very much appreciated.

Answer 1

http://img53.imageshack.us/img53/812/dif...

Answer 2

Product rule then chain rule

PR = [(x+4)^6]' * [(x+7)^2]  + [(x+4)^6] * [(x+7)^2]'

CR = 6(x+4)^5 [X+7)^2] + [(x+4)^6] * 2(x+7)

Answer 3

We know that if f(x)=g(x)^h(x) then taking natural logarithm from both sides of the eq. results in ln(f(x))=h(x)*ln(g(x)) so:

f'(x)/f(x)=h'(x)*ln(g(x))+h(x)*g'(x)/g...

--->f'(x)=(g(x)^h(x))*(h'(x)*ln(g(x))+...

Actually the question isnt so clear so I will consider three situations:

1)p(x)=(x+4)^(6(x+7)^2)) --->p'(x)=((x+4)^(6(x+7)^2)))*(12(x+7)*l...

2)p(x)=(x+4)^6+(x+7)^2---->p'(x)=6*(x+...

3)p(x)=((x+4)^6)*((x+7)^2)->p'(x)=6((x...

Answer 4

Here, we have a product of terms, (x+4)^6 and (x+7)^2. Thus, we will use the Product Theorem for Differentiation. Also, we will use the Chain Rule for differentiation for each term, since each term is a composition of a power function and a linear function.

p(x) = (x+4)^6 (x+7)^2

p'(x) = (x+4)^6 [2(x+7)(1)] + (x+7)^2 [6(x+4)^5 (1)]

p'(x) = (2x+14)(x+4)^6 + 6[(x+7)^2][(x+4)^5]