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 x1/2
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 = 4x3/2 + 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.
JR
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