Smart people- please help me solve this problem?

Question

f(x) = x+1/ sqrt x

derivative of x plus 1 divided by square root of x

I'm stuck on this one. Thank you for your help if you know how to solve it.

Answer 1

if by this you mean

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

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

or

f'(x) = (x^(3/2) - x^(1/2))/2

Answer 2

f'(x)=1-1/2 x^{-3/2}

Answer 3

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

Answer 4

(x+1)/sqrt(x)
= sqrt(x) + 1/sqrt(x)

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

using d/dx(x^n) = n x^(n-1)

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

d/dx(x^(-1/2)) = -(x^(-3/2))/2
add the two to get te result

Answer 5

f(x)=[x]+[1/(sqrt(x)]=[x]+[x]^-(1/2)

d(f(x))/dx=(d/dx)[x]+(d/dx)[x^(-1/2)]

=1+(-1/2)x^[(-1/2)-1]

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

Hope this helps

Answer 6

this might help you

http://www.ifigure.com/math/calculus/calculus.htm

http://www.hostsrv.com/webmab/app1/MSP/quickmath/02/pageGenerate?site=quickmath&s1=calculus&s2=differentiate&s3=basic

http://calc101.com/webMathematica/derivatives.jsp