Question

prove : d/dx(square root of u) is 1/2squareroot of u (du/dx)

Answer 1

isn't this direct application of chain rule?

Answer 2

Hint: definition of derivative

Answer 3

yeah you have to use the definition of derivative

Answer 4

how?

Answer 5

d (u)^1/2 dx = (d (u)^1/2 du) (du/dx)

Answer 6

d (u)^1/2 dx = (d (u)^1/2/ du) (du/dx)

Answer 7

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

Answer 8

then?

Answer 9

d (u)^1/2/ du = (1/2)(u)^(1/2 - 1)

Answer 10

and put the value of d (u)^1/2/ du in this
d (u)^1/2 dx = (d (u)^1/2/ du) (du/dx)