Question

d. find the derivative how to set up
y=log4(3x–2)3(7x2+5)

is the answer 1/[9(3x-2)^2(14x)]ln4

Answer 1

log base 4

Answer 2

Close, but you need to use the chain rule and the product rule.

Answer 3

On the inside of the log

Answer 4

which part is the chain rule for

Answer 5

I'll get ya started:
\[\frac{d}{dx}log_4(f(x)) = \frac{1}{f(x)ln4}\cdot \frac{d}{dx}f(x)\]

Answer 6

ty

Answer 7

So in this case f(x) is?

Answer 8

Oh wait a min

Answer 9

You need to be more clear with your brackets. Is the question this:
\[log_4[(3x–2)^3(7x2+5)]\]or\[log_4([3x–2]^3)\cdot (7x2+5)\]or\[log_4([3x–2])^3\cdot (7x2+5)\]

Answer 10

dont tell me i was right

Answer 11

yes first one

Answer 12

No you weren't right for sure. I'm just not sure what you're trying to solve. But either way you'd need the product rule and you don't have it.

Answer 13

So it's the log base 4 of the whole thing.

Answer 14

yes

Answer 15

Actually then the easiest thing to do is break up the product into a sum of logs.

Answer 16

\[log_4((a)^3(b)) = log_4(a^3) + log_4(b)\]

Answer 17

log4[(3x–2)3(7x2+5)] just for reference page is running out

Answer 18

Then differentiate term by term

Answer 19

using the chain rule. Also you can move that exponent inside into a multiplicative constant outside:

\[log_b(a^k) = k(log_b(a))\]

Answer 20

these are just standard logarithm rules, but they help make things easier so you don't have to fiddle as much with chain and product rules. You get the same result, but much faster.

Answer 21

the last part is the answer