what is the derivative of (sqrt of x+1)?

Question

i think it is 1 / 2*(sqrt x+1) but i dont get how it would

Answer 1

You want to find the derivative of (x+1)^(1/2) by the chain rule.

First find the derivative of the power using power rule. Multiply by the exponent and decrease the exponent by one. We get:

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

Next multiply by the derivative of the stuff inside the exponent (x+1) which equals 1. (Chain Rule)

Our final derivative is:

1/2 * (x+1)^(-1/2) or 1/(2*sqrt(x+1))

Answer 2

1/2 * (x+1)

Answer 3

i'll try to explain this one.

(sqrt of x + 1) is equal to (x + 1) raised to the 1/2 power.

According to derivative rules, you have to lower 1/2 and put it beside (x + 1), so that now it becomes 1/2(x + 1) [or in words, one-half times quantity x plus one].

I DON'T KNOW HOW THE RULE IS STATED BUT IT SOUNDS LIKE THIS: when you take the derivative of x raised to the nth power, multiply x by n and subtract 1 from n, so that now it becomes nx^(n-1) [or in words, n times x raised to the n - 1].

So we're not done yet. Going back to your problem, 1/2(x-1) now becomes 1/2(x-1) raised to the 1/2 - 1 or -1/2 [negative one-half]. Note that only (x-1) is raised to the -1/2 and 1/2 is not included.
so we now have, 1/2[(x-1)^(-1/2)].

Finally, (yes we're not done yet!) We have to take the derivative of (x-1) and multiply that to our last answer. It's called the chain rule. But since the derivative of (x-1) is just equal to 1, so our finally answer is indeed

1/2[(x-1)^(-1/2)], or in words, one-half times the quantity, x minus 1 raised to the negative one-half.

Hope you understood that. This one's relatively easy, though. Check out basic algebra books.

Answer 4

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

Answer 5

derivative of (sqrt(x+1))

this can be rewritten as

(x+1)^1/2

using diff(x^n)=n*(x)^n-1

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

Answer 6

d/dx (x + 1)^(0.5) = 0.5(x + 1)^(-0.5)

= 0.5/(x + 1)^0.5

Note that sqrt is equivalent to the -1/2 pwr and,

(x + 1)^(-1/2) = 0.5/(x + 1)^1/2

used 0.5 for 1/2 in the equation to keep it simple.


So your answer is correct.

Answer 7

___1___
2(sqrt x+1)

Answer 8

(X+1)^(0.5)

Derivative = 0.5*(X+1)^(-0.5)