Find, w.r.t to x, both the derivative and integral of y=6*sqrt(x)

Understand the question:

'w.r.t' stand for 'with respect to', so the qestions is asking for the dericative and integral to be calcuated in terms of x - so find dy/dx and (integral sign) y dx. 

Sqrt(x) is the same as x^1/2

Deriative

Bring power to the front and decrease the power by one: dy/dx = 61/2x^(1/2)-1 = 3x^-1/2

Integral

Increase the power by one and divide by the new power: I = 6/((1/2)+1)*x^(1/2)+1 = 4x^3/2 + C

IF YOU ARE DOING A DEFINATE INTEGRAL (ONE WITHOUT LIMITS) NEVER FORGET TO PUT + C (PLUS CONSTANT. This is a very easy way to drop a mark.