Question

differentiate function

y=x^2 + 4x +3/(square root of x)

Answer 1

2x+4 -(3/2)x^(-3/2)

Answer 2

nothing is being multiplied so each is the power rule. ax^n = anx^(n-1) is the general formula for each where a is what is in front of x, x is the variable, n is the power

Answer 3

Davidjohn wait a sec, you have to use the quotient rule here

Answer 4

for the last one 3/x^1/2 is
3x^-1/2
\[3(-1/2)x^ ((-1/2)-(2/2))\]

Answer 5

Oh it depends, is it
y=x^2 + 4x +3/(square root of x)
or
y=(x^2 + 4x +3)/(square root of x)
?

Answer 6

no there is no variable times a variable in the numerator or denominator. right if it were that then you would

Answer 7

but i helped this person before and most were power rule so im assuming that this is too

Answer 8

both of them have a parenthesis Andras

Answer 9

So you need
d/dx(x^2 + 4x +3)/(square root of x) ?

Answer 10

but the top one has parenthasis in the numerator which would make the whole top term divided by the bottom rather than just the +3

Answer 11

yes

Answer 12

Ok than you need to know that
(f(x)/g(x))'={f'(x)*g(x) -g'(x)f(x)}/g^2(x)

Answer 13

I guess david is doing it for you

Answer 14

andras, the x^1/2 would be positive right? in the quotient rule

Answer 15

The rule is there
here f(x)=x^2 + 4x +3
and g(x)=sqrt(x)

Answer 16

okay then, just making sure :) thanks

Answer 17

So f'(x)=2x+4
g'(x)=1/2 x^(-1/2)

Answer 18

yeah and the g(x)^2 would just be x

Answer 19

so, ((2x + 4)(x^1/2)-(x^2 + 4x + 3)(1/2x^-1/2))/ (x)

Answer 20

{(2x+4)(sqrtx)-(x^2+4x+3)(1/2x^(-1/2))}/x

Answer 21

yes

Answer 22

now I guess this can be rearranged into a simple form

Answer 23

haha true, but didnt want to do ALL the work ;)

Answer 24

ok :-) Lets leave it than?

Answer 25

Dany are u happy?

Answer 26

okay you all confused me, so whats the answer o.O

Answer 27

{(2x+4)(sqrtx)-(x^2+4x+3)(1/2x^(-1/2))}/x

Answer 28

I need pen and paper to rearrange this into a simple form and I cannot be asked to search for one now :-)

Answer 29

it all together, when you have a variable function divided by another function the rule is

(f(x)/g(x))'={f'(x)*g(x) -g'(x)f(x)}/g^2(x)

here f(x)=x^2 + 4x +3
and g(x)=sqrt(x)

So f'(x)=2x+4
g'(x)=1/2 x^(-1/2)

if put all together from andras and i, mostly the former
((2x + 4)(x^1/2)-(x^2 + 4x + 3)(1/2x^-1/2))/ (x)
which i will simplify in a minute

Answer 30

oh so i use the other rule, i was thinking i had to do the power rule.

Answer 31

you would have to only if the whole numerator was not in parenthesis because then it would be just constants times a variable

Answer 32

well in the paper it has the polynomial all divided by the square root of x

Answer 33

y=x^2 + 4x +3/(square root of x) is power rule

y=(x^2 + 4x +3)/(square root of x) is quotient rule

Answer 34

but i dont think i have that rule yet in my notes in which we are doing this, all i have is the constant, power, and d/dx[cf(x)]=cf'(x)

Answer 35

\[y'(x) = -\frac{3}{2 x^{3/2}}+2 x+4\]

Answer 36

that is what i put first but i guess the whole function is divided by the x^.5

Answer 37

\[y(x) = \frac{x^2 + 4x +3}{\sqrt{x}}\]
\[y'(x) = \frac{3 x^2+4 x-3}{2 x^{3/2}}\]