Question

find the derivatives :
d/dx[(x^2+1)sin√x]

Answer 1

\[(x^2 + 1) \sin \sqrt x\]
use product rule

\[(x^2 + 1) \frac{d}{dx} (\sin \sqrt x) + \sin \sqrt x \frac{d}{dx} (x^2 + 1)\]

Answer 2

so where are you having trouble?

Answer 3

i dont even know where to start :/

Answer 4

You also need the chain rule for d/dx sin( sqrt (x))

Answer 5

so how do i do that?

Answer 6

first of all do you know product rule?

Answer 7

yes

Answer 8

so do you agree with my set up above?

Answer 9

yes

Answer 10

so your only problem is \[\frac{d}{dx} \sin \sqrt x\]
and
\[\frac{d}{dx} (x^2 + 1)\]

Answer 11

so what's \[\frac{d}{dx} \sin \sqrt x\]

Answer 12

i got the same thing that she did

Answer 13

and now it is gone

Answer 14

but isnt it cos sqrtx

Answer 15

something is missing

Answer 16

you need to get the derivative of sqrt x furthermore

Answer 17

how do i do that?

Answer 18

?

Answer 19

what is the derivative of sqrt x?

Answer 20

x^-1/2

Answer 21

is that right?

Answer 22

no..what did you do?

Answer 23

oh i for got to multiply the front

Answer 24

1/2 x ^-1/2

Answer 25

better

Answer 26

ok so how does that go into the problem?

Answer 27

so the \[\frac{d}{dx}\sin \sqrt x \implies \cos \sqrt x (\frac{1}{2\sqrt x}\]

Answer 28

or in nicer words \[\frac{\cos \sqrt x}{2\sqrt x}\]

Answer 29

ok so where are we in the problem so far?

Answer 30

like from the beginning

Answer 31

?

Answer 32

now you have to find \[\frac{d}{dx} (x^2 + 1)\]

Answer 33

ok so thats not my answer is it? sorry im really confused

Answer 34

it's not

Answer 35

remember we have \[(x^2 + 1) (\frac{d}{dx}[ \sin \sqrt x) + \sin \sqrt x (\frac{d}{dx} (x^2 + 1))\]

Answer 36

we already hae d/dx sin sqrt x

Answer 37

ok so where do we go from there.. i think it might be easier if you would write the whole process out and then explain it as a look at it if you could do that? sorry im just very visual learner

Answer 38

from where?

Answer 39

from the last thing that you wrote the long equation

Answer 40

that was just the thingy a while ago

\[\frac{d}{dx} [(x^2+1)(\sin \sqrt x)] = (x^2 + 1)[\frac{d}{dx} (\sin \sqrt x)] + (\sin \sqrt x)[\frac{d}{dx} (x^2 +1 )]\]
that's just the product rule

Answer 41

the first step to solving this is \[\frac{d}{dx} (\sin \sqrt x)\]
we already did this correct?

Answer 42

yeah

Answer 43

btw...that's the first step because that's the thing we dont know

Answer 44

what do you think is the second thing we dont know?

Answer 45

ok

Answer 46

what x is?

Answer 47

nope...that's not really important

Answer 48

look at the product rule

Answer 49

oh

Answer 50

what's the second thing you dont know in the product rule?

Answer 51

d/dx?

Answer 52

d/dx of what?

Answer 53

x^2+1

Answer 54

right. so what's \[\frac{d}{dx} (x^2 + 1)\]

Answer 55

2x

Answer 56

right so now substitute

Answer 57

substitute the value of \[\frac{d}{dx} \sin \sqrt x\] and the value of \[\frac{d}{dx} (x^2 + 1)\]
into
\[(x^2 + 1) \frac{d}{dx} (\sin \sqrt x) + \sin \sqrt x \frac{d}{dx} (x^2 + 1)\]

Answer 58

2x(1/2 cos ^-1/2)+(1/2 cos ^-1/2)(2x)

Answer 59

?

Answer 60

i dont think that is right

Answer 61

would it be (x^2+1)(1/2 cos ^-1/2)+(sin sqrtx)2x

Answer 62

what did you do?

Answer 63

substituted

Answer 64

where are the x

Answer 65

huh?

Answer 66

(x^2+1)(1/2 cos ^-1/2)+(sin sqrtx)2x

where's the x on that cos thingy

Answer 67

would it be (x^2+1)(1/2 cosx ^-1/2)+(sin sqrtx)2x

Answer 68

?

Answer 69

can you draw it?

Answer 70

draw what?

Answer 71

your answer

Answer 72

\[x ^{2}+1(1/2\cos ^{-1/2})+(\sin \sqrt{x})(2x)\]

Answer 73

no...not the equation...the draw tbutton...draw your answer

Answer 74

isnt that my answer?

Answer 75

because there's no such thing as \[\cos^{-1/2}\]

Answer 76

im looking for x...idk where you placed it

Answer 77

look at what i said \[\frac{d}{dx} \sin \sqrt x\] again

Answer 78

cosx^-1/2

Answer 79

what else? that's incomplete

Answer 80

look at the post where i said what d/dx sin sqrt x is

Answer 81

do you mean the 1/2 infront?

Answer 82

what did i say d/dx sin sqrt x was?

Answer 83

cos√x
/2√x

Answer 84

can you see the difference with what you wer saying a while ago?

Answer 85

yupp

Answer 86

so what's the complete correct answer now?

Answer 87

\[x ^{2}+1(\cos \sqrt{x}/2\sqrt{x})+\sin \sqrt{x}(2x)\]

Answer 88

right \[\large \frac{(x^2+1)(\cos \sqrt x)}{2\sqrt x} + 2x\sin \sqrt x\]