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How do you differentiate x times the square root of x minus 1 with respect to x?
Wiki User
∙ 13y ago
f(x)=(x(x-1)^.5) dx
Look at the equation in pieces. Piece A is x, and Piece B is ((x-1)^.5)dx
The derivative will be the derivative of piece A times Piece B all added to the derivative of piece B times Piece A. So we will need to find the derivative of each individual piece to find the solution.
The derivative of Piece A is 1.
Use the u-substitution method of differentiation to find the derivative of Piece B.
Have u=(x-1), causing du to equal dx. The derivative of (u^.5) is dx/2(u^.5)
Substitute the original piece back in to give you 1/2(x-1)^.5
So the derivative of the original function would be...
(1 times (x-1)^.5) + (x times (1/2(x-1)^.5) all times dx
The only thing you can really do to simplify that would be to replace the 1 in the final fraction with the x that you are multiplying it by.
Wiki User
∙ 13y ago
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