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 4x^3-1= 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

((x^2+4x)/2x)-((x^2-4x)/x)

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differentiate y=(4x^3)-5/x^2

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