differentiate y=(4x^3)-5/x^2
to differentiate this equation we have to do it in two parts because there is a minus sign seperating them in the middle
for the first part we first have to multiple the constant by what the power of x is which is 3, secondly we have to minus 1 from the power
dy/dx = 3 x 4x3-1= 12x2
the second part is slightly harder as the x is on the bottom, to get around this we can write it as
y = 5/x^2 = 5x^-2
when the x is on the bottom it is the same as having the x on top with a minus sign infront of the power
we then do the same as in the first part which is multiple the constant at the front by the power above the x including the minus sign and minus one from the power
dy/dx = -2 x 5x-2-1 = -10x-3
we then have to combine the two halves of the equation without forgetting the minus sign in between which cancels out because there are now two negatives which equal a positive so we get
dy/dx = 12x2 + 10x-3
we can simplify this to
dy/dx = 12x2 + 10/x3
this is the prefered form
as you can see we can swap the x with the minus power to the bottom to make it a positive power again
