Find the derivative of f(x) = x + (sq. root of x)??

Question

Find the derivative of f(x) = x + (sq. root of x)??

I know we use f(x+h)-f(x) / h
but get lost doing the conjugates to solve, etc?????? help pls!

Answer 1

use techniques on differentiation

just get the derivatives of each individual factors

derivative of x is 1

derivative of sq. root of x = 1/2(sq. root of x)

so derivative of x + (sq. root of x) = 1 + 1/2(sq. root of x)

Answer 2

Well you can use chain rule for differentiating them. This is an easy equation but I am guessing that this is your first time with calc. OK so lets take this step by step.

- Since this is x + root of x, or this is an "addition" polynomial, so we can differentiate each part indivdually.

- First lets do x. The formula is n * x^(n-1). So in this case, n=1. Thus it becomes 1*x^0 which is just 1.

- Secondly the root of x. This in other word is x^(1/2). So the same rule again and it gives us (1/2)*x^(1-1/2) which is 1/2*(root of x).

- Finally we just add both to give us 1+ 1/2*(root of x).

Answer 3

i may be wrong, but if my calculus is right, the answer is 0=0+sqr of 0 x becomes zero due to the first power going to o and thus the square root of x to the zero power is also 0. a math pro will probably tell you i'm wrong, but i haven't done a derivative in over 25 years. here's hoping i get something right.

Answer 4

If you have a math book to help you it will explain techniques of differentiation in which f(x) = x becomes f'(x) = nx^(n-1)

So you get f'(x)= 1 + (1/2)(x)^(-1/2)

one plus one-half x to the negative one-half.

Answer 5

assume (x+a million)=t squaredifferentiating the two components, we get dx=2t dt :. ln (a million/(x squareroot (x+a million)=In (2t/(tsq -a million)t) t cancels from numerator and denominator and then we use the identification for In (2/(tsq -a million)) ans is 2log(t-a million/t+a million)...then placed x+a million back incredibly than t for extremely final ans!

Answer 6

f(x) = x + sqrt(x)
f(x) = x + x^(1/2)

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

ANS : f'(x) = 1 + (sqrt(x)/4) or (4 + sqrt(x))/4

Answer 7

lim( f(x+h)-f(x))/h = (h)+sqrt(x+h)-sqrt(x)/h
h-0
use expansion of sqrtx and solve.