Find the derivative of the function.
g(x) = (2 + 3x)^4(4 + x - x^2)^7...this is awefully long to substitue...

Question

amistre64 · Answer

g(x) = (2 + 3x)^4(4 + x - x^2)^7

its product rule; power rule; and chain rule applications

anonymous · Answer

i got it up to (2+3x)^4*7(4+x-x^2)^6+(1-2x)+(4+x0x^2)^7*4(2+3x)^3*3.....

amistre64 · Answer

l = (2+3x)^4  ;  l' =  12(2+3x)^3

r = (4+x-x^2)^7  ;  r' = 7(4+x-x^2)^6 (1-2x)

anonymous · Answer

yes..i went through that

amistre64 · Answer

$$g'=(2+3x)^4.(7-14x)(4+x-x^2)^6 + (4+x-x^2)^7.12(2+3x)^3$$

amistre64 · Answer

how compact are you trying to get it?

anonymous · Answer

til i cant solve no more

amistre64 · Answer

$g' =$

       $ (7-14x).(4+x-x^2)^6.(2+3x)^4$

            $  + 12(2+3x)^3.(4+x-x^2)^7 $

the only other thing to do is expand it all out and see what combines

amistre64 · Answer

but that is usually NOT done since it is easier to work it in this form

anonymous · Answer

ok ill take it from here thanks again : )

amistre64 · Answer

youre welcome :)

anonymous · Answer

$$5^{x+4}=7^{x}$$

anonymous · Answer

Can anyone tell me how to solve this to the nearest thousandth.

amistre64 · Answer

odd place to post it, but maybe

amistre64 · Answer

(x+4) ln(5) = x ln(7)

(x+4)/x = ln(7)/ln(5)

1+4/x = ln(7)/ln(5)

4/x = [ln(7)/ln(5)] -1

x = 4/{ln(7)/ln(5)] -1}

$$x = \frac{4}{\frac{ln(7)}{ln(5)}-1}$$

amistre64 · Answer

19.133 i think