Question

first derivative!

Answer 1

\[x \sqrt{9-x}\]

Answer 2

Use the product rule...

Answer 3

dy/dx=f'(x)g(x)+f(x)g'(x)

Answer 4

Here, I will get you started

Answer 5

(x)'(sqrt9-x)+(x)(sqrt9-x)'

Answer 6

dy/dx=(x)'(sqrt9-x)+(x)(sqrt9-x)'

Answer 7

Are we clear so far?

Answer 8

here, I will give you a hint as well..\[ \sqrt{9-x}=(9-x)^{1/2}\]

Answer 9

yeah i knew all that i just needed help with simplifying i got \[\frac{ x \sqrt{9-x} }{ 2\sqrt{9-x} }\]

Answer 10

which is x/2

Answer 11

am i on the right track or?

Answer 12

no, your simplification is incorrect

Answer 13

gahhh...my equation application for this text box is not working for some reason...hold on

Answer 14

then where do i go from \[(x) \frac{ 1 }{ 2 }(9-x)^{\frac{ -1 }{ 2}} + (9-x)^\frac{ 1 }{ 2 }\]

Answer 15

your calculations should have lead you to that point...

Answer 16

why is it minus

Answer 17

\[dy/dx=(x)'(\sqrt{9-x})+(x)(\sqrt{9-x})'=\sqrt{9-x}-\frac{x}{2\sqrt{9-x}}\]

Answer 18

you have to take the derivative of 9-x (chain rule) when computing the derivative of sqrt(9-x) which is -1

Answer 19

Now you must solve algebraically...

Answer 20

oh okay that is what I forgot

Answer 21

I have the fonal answer, let me know when you come to yours and post it so I may confirm...

Answer 22

*final

Answer 23

\[-\frac{ 3x+18 }{ 2\sqrt{9-x} }\]

Answer 24

?

Answer 25

very close...

Answer 26

is it just x in the nominator then?

Answer 27

everything is correct except the numerator...

Answer 28

the numerator is as follows:
3(x-6)

Answer 29

everything elses you had was correct

Answer 30

check you calculations and see where you made a small error

Answer 31

you just factored out the 3

Answer 32

your sign is incorrect...had i written it in your notation it would look like this...

Answer 33

woops i had the negative right on my piece of paper i just typed in +18

Answer 34

cool, nice work

Answer 35

wait actually why is it negative

Answer 36

the whole function or the minus in the numerator?

Answer 37

minus in numerator

Answer 38

you should have gotten 2(9-x)-x in the numerator when you solved algebraically...

Answer 39

my work

Answer 40

when you subtracted the two fractions

Answer 41

here...

Answer 42

solve it this way..it is much easier...

Answer 43

that is (a/b)-(c/d)=(bd) to solve algebraically

Answer 44

clear?

Answer 45

no not really