Verified answer

well lets first simplify the problem by using indices rules ( add the powers)

y=x^2.5

differentiate with respect to x so you get

dy/dx = 2.5x^1.5

sub in x (which is 1)

dy/dx = 2.5 this is your gradient

hope i could have been of help. ( your question seems to suggest you want the equation of the tangent is this so?)

Not sure what you're trying to write out there. If its x^2 multiplied by sqrt(x) then this is equal to y=x^2.5.

You then need to differentiate the equation. dy/dx = 2.5x^1.5

Then sub in x=1, and dy/dx=2.5 at x=1,

So the gradient at that point is 2.5