Having trouble knowing when my derivative is fully simplified.

[hopelynnwelch]

f(x)=3^(x-2)+9^(x+1)

I'm wondering if my answer is simplified and complete enough like this.

f'(x)=3^(x-2)*ln3*1+9^(x+1)*ln9*1

f'(x)=3^(x-2)*ln3+9^(x+1)*ln9

Once again looking at a derivative calculator and they are much different then I. Sorry my teacher is a simplification NUT and I just want to try to figure out why I am always getting points off for not simplifying completely. I want to make sure i am doing these correctly.

View attachment 32745

Any help appreciated!
Thank you!

 

[Steven G]

f(x)=3^(x-2)+9^(x+1)

I'm wondering if my answer is simplified and complete enough like this.

f'(x)=3^(x-2)*ln3*1+9^(x+1)*ln9*1

f'(x)=3^(x-2)*ln3+9^(x+1)*ln9

Once again looking at a derivative calculator and they are much different then I. Sorry my teacher is a simplification NUT and I just want to try to figure out why I am always getting points off for not simplifying completely. I want to make sure i am doing these correctly.

View attachment 32745

Any help appreciated!
Thank you!

I think this is fine as is. You can factor out ln(3). You can get the bases to be both 3 and factor 3 to some power out. If you show us the final answer I am sure someone will show you how to proceed with your current result.

 

[hopelynnwelch]

I think this is fine as is. You can factor out ln(3). You can get the bases to be both 3 and factor 3 to some power out. If you show us the final answer I am sure someone will show you how to proceed with your current result.

Ohh sorry. Here is the calculators result and why I'm not sure if my answer is simple enough.

 

[Steven G]

f(x)=3^(x-2)+9^(x+1)

I'm wondering if my answer is simplified and complete enough like this.

f'(x)=3^(x-2)*ln3*1+9^(x+1)*ln9*1

f'(x)=3^(x-2)*ln3+9^(x+1)*ln9

Once again looking at a derivative calculator and they are much different then I. Sorry my teacher is a simplification NUT and I just want to try to figure out why I am always getting points off for not simplifying completely. I want to make sure i am doing these correctly.

View attachment 32745

Any help appreciated!
Thank you!

I think this version of the answer is stupid and I never said that before!
OK here goes.3^(x-2) = (3^2)(3^(x-2))/3^2 = (3^x)/9
9^(x+1) = 9*9^(x+1)/9 = 9^(x+2)/9
Can you put this all together from here?

 

[Steven G]

f(x)=3^(x-2)+9^(x+1)

If simplifying was my main concern I would write f(x) as f(x) = 3^(x-2) + 3^(2x+2). At least this way I will definitely have ln(3) to factor out. Actually very very quickly we obtain f'(x)= ln(3)(3^(x-2) + 2*3^(2x+2))

 

[hopelynnwelch]

so would you say that


3ln3(1^(x-2)+2^(2x+2))

is simplified?

 

[Steven G]

so would you say that


3ln3(1^(x-2)+2^(2x+2))

is simplified?

Even your answer is not simplified since 1^(x-2)=1 and 2^(2x+2)=4^(x+1).
But what you did is all wrong!
In say 4*5^3 why would the power 3 ever become the power of the 4??. Just because I factor out a 5, the power 3 is NOT the power of the 4. 4*5^3 = 5(4*5^2)

Maybe you can factor out 3^(x-2). But again, your original answer is fine. Sometime (but not always)how one factors is a matter of their own style. I am positive if you gave this problem to a handful of people you would get a handful of answers. On this problem do not stress out over simplifying. You will end up losing points on an exam by making mistake trying to (unnecessarily) simplify.