Question

derivative of (x)/(x^2 + 5)

please show work

thanks in advance

Answer 1

are you familiar with the "quotient rule"?

Answer 2

no just beginning calc

Answer 3

what about \[\lim_{h \rightarrow 0} \frac{f(x+h) - f(x)}h\]
familiar?

Answer 4

thats defination of derivative right

Answer 5

kimmy can you help me pls

Answer 6

Use this young man:
\[\frac{d}{dx}(\frac{u}{v})=\frac{u'v-uv'}{v^2}\]
Where u' and v' means du/dx and dv/dx.

Answer 7

would you mind demonstrating that pls? i just started calc and my teacher isnt a good english speaker

Answer 8

I can't, i'm not in my mood to work something myself. But I can help you.
Can you show me what is u and v in your problem?

Answer 9

u is numerator v is denominator

Answer 10

yes, correct. In this case, what is u and v?

Answer 11

u= x and v= x^2 - 5

Answer 12

what about u' and v'?

Answer 13

u'= 1?
v'= 2x?

Answer 14

Correct.. Now plug al these into my "young man" equation.

Answer 15

(1*x^2-5 minus x * 2x)/(x^2 - 5)^2

Answer 16

??

Answer 17

Almost corret, missed one sign

Answer 18

not sure where

Answer 19

-5
isn't it +5

Answer 20

Your v should be x^2+5

Answer 21

right.

so whats next?

Answer 22

that's the answer. the first derivative of the function with respect to x.

Answer 23

how come wolfram says different
http://www.wolframalpha.com/input/?i=derivative+of+%28x%29%2F%28x%5E2-5%29

Answer 24

Did you spot you typed different function? i see you write x^2-5 at wolfram

Answer 25

crap. i just noticed. its supposed to be x^2 - 5 sorry

Answer 26

then v=x^2-5

Answer 27

huh

Answer 28

Show respect to your teacher :)
What's your final answer.

Answer 29

(1*x^2-5 minus x * 2x)/(x^2 - 5) ??

Answer 30

yes,
=x^2-5-2x^2/(x^2-5)
=-x^2-5/(x^2-5)
=then you can proof wolfram's right with this

Answer 31

ahh i see thanks

Answer 32

one last one

Answer 33

derivative of f(x)= (x^4 + x)^3 (x^2 - 1)^2

Answer 34

d(u*v)/dx = u'v+uv' ..........................(2)
You know the routine:
determine u and v,
find u' and v'
plug all these into (2).
Show me your final answer.

Answer 35

im confuse as to how to take the derivative with the exponent oustide the paranthesis

Answer 36

Ex:
d(u)^5/dx = 5*(u)^(5-1) * d(u)/dx

Answer 37

so 3 * (4x) (2x) * 2?

Answer 38

Nope, what's u'?