Question

Derive: w = Square root of (x^2 · 5^x )3 :

So this is what I did:

((x^2 + 5^x)^3)^1/2 =

(x^2+5^x) =

3/2(x^2 + 5^x)^1/2 (2x* 5^x + ln(5))

Answer 1

BOB ( Bac of the book) has a different answer, here is my question, do I have to take the derivative again of (x^2 + 5^x) ?

Answer 2

back*

Answer 3

Is it because it's a product rule ? I think that's what I was missing.

Answer 4

hey :)

Answer 5

wait is that a dot or+ between the two terms ??

Answer 6

@Issy14

Answer 7

it's a , which two terms?

Answer 8

it's a * times (multiplication)

Answer 9

so if it was a multiplication why did u write it as addition ?

Answer 10

\[w=\sqrt{(x^{2}*5^x)^3}\]

Answer 11

that's what it is

Answer 12

that's the original.

Answer 13

\[\large \sqrt{(x^2 · 5^x )^3}\]

Is this your question?

Answer 14

sorry, wrong sign all the way

Answer 15

ok first u have to write it like this \[(x ^{2}.5^{x})^{\frac{ 3 }{ 2}}\]

Answer 16

Is there \(\cdot\) or \(+\) ??

Answer 17

so this is what i came up so far with: 3/2(x^2* 5^x) (2x)(5^x) + (5^x * ln(5) (x^2)

Answer 18

yup u wrote it as addition in the second step then u derived it as addition and that's why ur answer is wrong

Answer 19

I truly apologize for the mishap

Answer 20

You have to subtract also in the power, 3/2 you are carrying forward, and then you will do (3/2) - 1 in the power..

Answer 21

I did that, at the beginning: I ended up with 1/2 so 3(x^2*5^x)^1/2 and I proceeded from there

Answer 22

Wait, please write your final answer or the step where you have reached till now..

Answer 23

3/2(x^2* 5^x) (2x)(5^x) + (5^x * ln(5) (x^2)

Answer 24

Why you are not taking exponent there???

Answer 25

exponent there in 3/2(x^2* 5^x)^1/2 (2x)(5^x) + (5^x * ln(5) (x^2)

Answer 26

Yep...

Answer 27

And please be careful with brackets..

At last, you have applied product rule which contains two terms, so first term upto ..........^1/2, after this brackets will start...

Answer 28

got it, but then the back of the book has a different answer and I don't know how they got there

Answer 29

\[\large \color{green}{\implies \frac{3}{2}(x^2* 5^x)^{\frac{1}{2}} [(2x)(5^x) + (5^x * \ln(5) (x^2)]}\]

Answer 30

Sorry, in excitement, I wrote somewhat big there...!!! :)

Answer 31

Yes, that's what I have so far, that's where I stopped. I don't know how to proceed from there.

Answer 32

hahahahhaha it's ok, I like math too, it makes think and be patient.

Answer 33

Now, tell me what your BOB, I mean what your back of book says..

Please write that answer too..

Answer 34

Just for the record, are you SURE that "derive" is a imperative form synonymous with "find the derivative"?

Answer 35

ok, one second BOB says: 3/2 x^2 square root of 5^2x (2 + x ln(5))

Answer 36

If they factored, idk where they got the common factor from

Answer 37

Is that 5^(2x) there??

Answer 38

yes =(

Answer 39

And you should be happy that you have done absolutely right...

Answer 40

so it's BOB crazy?

Answer 41

nuuuuu, don't say that, sometimes BOB has been known to be wrong

Answer 42

Oh sorry, you must be happy now that we are absolutely and perfectly right... Sorry, I did not read the BOB answer carefully... Yes we are right, just we have to rearrange our reached answer..

Answer 43

hahhahahaha...

Answer 44

See, this you know:

\[\large (a \cdot b)^x = a^x \cdot b^x\]

Answer 45

And now just take \(x \cdot 5^x\) common from the brackets... And see what you get..

Answer 46

And you must be knowing:

\[\large (a)^{\frac{1}{2}} = \sqrt{a}\]

Answer 47

5x? shouldn't it be 5^x that's what you meant right?

Answer 48

\[\large (x^2 \cdot 5^x)^{\frac{1}{2}} = (x^2)^{\frac{1}{2}} \cdot (5^x)^{\frac{1}{2}}\]

Answer 49

ok, one second let's see.

Answer 50

Where???

Answer 51

Ha ha ha ha... :P

Answer 52

Where you have seen 5x ??? Open your eyes, there is no 5x anywhere... :)

Answer 53

omg, I think I finally lost it.

Answer 54

See do step by step..

Answer 55

BOB was right once again... it's a hate-love relationship. 3/2 x^2 square root 5^x ( 2 + ln(5))

Answer 56

You got it or not??

Answer 57

Yeah I got it. I wrote it on my whiteboard

Answer 58

Okay, that's nice.. :)

Good Luck...!!!

Answer 59

And Well Done!!!

Answer 60

Thank you!!! my brain is sore like a muscle, I'm going to drink water.

Answer 61

Okay!!

Answer 62

Except that \(\sqrt{x^{2}} = |x|\) in the absence of additional information.