Derivatives?

Question

Can someone help me figure out this one problem??

square root of x+1/x^3

thanks..

sorry i wrote it wrong..

(square root of x) + (1/x^3)

Answer 1

f (x) = x^(1/2) + x^(-3)
f `(x) = (1/2)x^(-1/2) - 3x^(- 4)
f `(x) = 1 / ( 2x^(1/2) ) - 3 / x^4

Answer 2

1/3x^2 / 2square root of x+1/x^3

Because derivative of x+1 is 1
derivative of x^3 is 3x^2
and derivative of square root is :
derivative of the thing inside the root / 2 multiplied by the root
(2 because it is square)

Answer 3

since sqrt of x=x^-1 and 1/x^3=x^-3
then using the basic principle,
x^-1+x^-3
=-x^-2-x^-4
=-1/x^2-1/x^4