anonymous
  • anonymous
find the derivative of g(x)= 4sqrt(x)+3
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
is it just sqrtx
lalaly
  • lalaly
\[\large{g'(x) =4 \times \frac{1}{2} x^{\frac{-1}{2}}} = \frac{2}{\sqrt{x}}\]
anonymous
  • anonymous
i think it would be 2/sqrt(x)

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
first convert the square root to a fractional index = 4x^(1/2) + 3 derivative = 4 * (1/2) x ^(1/2 - 1) = 2 x(-1/2) or 2 / sqrtx
anonymous
  • anonymous
why did you have (1/2-1)...where did the -1 come from?
anonymous
  • anonymous
we used the general formula for the derivative of if f(x) = ax^n f'(x) = an x^(n-1)
anonymous
  • anonymous
oh ok thanks
anonymous
  • anonymous
yw
anonymous
  • anonymous
jimmy could you help me with this one...its confusing. A girl standing on the top of a building 200 feet highs throws a water balloon up in the air at a velocity of 30ft/sec. The equation for the height of the water balloon is h(t)=-16t^2 +30t + 200 find the instantaneous velocity at two seconds and the direction of the water balloon
phi
  • phi
instantaneous velocity is dh/dt take the derivative with respect to t to get a new equation then sub in t=2 to find the velocity
phi
  • phi
if you get +, the balloon is going higher. if you get a negative number, the balloon is falling
anonymous
  • anonymous
can someone please demonstrate that
phi
  • phi
find the derivative term by term use if f(t) = a*t^n f'(t) = a*n* t^(n-1) just like Jim did up above
phi
  • phi
h(t)=-16t^2 +30t + 200 first find the derivative of -16 t^2 using the rule
anonymous
  • anonymous
-32t + 30t + 0??
phi
  • phi
check derivative of 30t
anonymous
  • anonymous
30t is already reduce, isnt it?
phi
  • phi
you start with -16t^2 +30t + 200 then term by term 2* -16 * t^ (2-1) 30*1* t^(1-1) 200 * 0 * t(0-1)
phi
  • phi
remember t^0 is 1
anonymous
  • anonymous
oh i see so when i have -32t + 1 + 0...do i just plug in 2 to find the instantaneous velocity into t
phi
  • phi
of course nobody uses the exponent rule to find the derivative of a constant. We know it is zero.
phi
  • phi
now recheck : derivative with respect to t of : 30 t = ??
anonymous
  • anonymous
t^0= 1 therefore, 30t = 1?
phi
  • phi
use the rule: d/dt (30 t^1) = 1*30*t^(1-1) = 1*30*1 = ??
anonymous
  • anonymous
just 30
phi
  • phi
so the derivative of -16t^2 +30t + 200 = ?
anonymous
  • anonymous
-32t + 30 + 0
phi
  • phi
adding 0 is not usually done . I mean leave it off, because it does not change anything
phi
  • phi
so now you have h'(t) = -32t + 30 change in height with respect to time (velocity for this problem= -32t + 30
phi
  • phi
find the instantaneous velocity at two seconds and the direction of the water balloon this means replace t with 2 in your equation to find the velocity at time t=2
anonymous
  • anonymous
ok i did and i got -34
phi
  • phi
you got -34 ft/sec (don't forget the units) the negative sign means which direction? Here is how we know which direction: A girl throws a water balloon *up* in the air at a velocity of +30ft/sec. The problem says +30ft/sec is up, so a -34 ft/sec must be which direction?
anonymous
  • anonymous
down
phi
  • phi
I hope it makes sense. But you have answered the entire question.
anonymous
  • anonymous
yeah it really did. thanks for taking the time.
anonymous
  • anonymous
to teach me

Looking for something else?

Not the answer you are looking for? Search for more explanations.