derivative of 3root x?

Question

im not sure how to do the derivative of 3rootx..
i know root x is = x^(-1/2)
but how about with 3 infront?

Answer 1

i'm giving u the general formula

derivative of x^n=nx^(n-1)

then, x^(1/3)
=1/3. x^(1/3 -1)
=1/3. x^(-2/3)

Answer 2

The 3 is just a constant and can be ignored until the end. Also the deriv of root of x is NOT x^(-1/2), it is x^(-1/2)*(1/2). I learned it as the root of x is 1 over 2 root x. It is just like x^2. To find its deriv, you just put the exponent in front and subtract 1. It is 2x^(2-1)=2x. So the deriv of x^(1/2) is just (1/2)x^(-1/2). Then at the end multiply that by 3.

Answer 3

One thing that derivatives, integrals, and limits have in common are that you can always ignore the constant

For instance, if
f(x) = 7x^2, then f'(x) = 7(2x) = 14x, and if
f(x) = 6sinx, then f'(x) = 6cosx

It's no different here. If f(x) = 3*x^(1/2), then f'(x) = 3 [(1/2)x^(-1/2)], or, if you want to simplify

f'(x) = 3 / [ 2 x^(1/2) ]

(It's proper mathematical etiquette not to have negative exponents, though you're unlikely to lose marks over that on a Calculus test)

Answer 4

are you talking about the 3 in front of the x or in front of the negative 1/2

Answer 5

Root x is x^(1/2), not x^(-1/2).

d/dx 3x^(1/2) = (3/2) x^(-1/2)

The answer is 3/(2 sqrt(x)).

Answer 6

root(x) = x^(1/2), not x^(-1/2)

3sqrt(x) = 3x^(1/2)

the derivative of this is

(3/2)x^((1/2) - 1)

(3/2)x^(-1/2)
3/(2sqrt(x))
3/(sqrt(4x))
(3sqrt(4x))/(4x)
(6sqrt(x))/(4x)
(3sqrt(x)/(2x)

ANS : (3sqrt(x))/(2x)