The curve C has equation y = 3x^4 – 8x^3 – 3. Find dy/dx.
To find dy/dx, the differential, of any function... you must times the coefficient of each variable of x by its power, then reduce the power by one. Using this information we can work out that 3x^4 turns to 12x^3, and -8x^3 turns to -24x^2. Since -3 doesn't appear to be a coefficient of x, we must imagine it to be -3x^0. Therefore when you multiple the coefficient, 3, by 0, this part of the equation turns to zero.
Therefore if curve C has equation y = 3x^4 – 8x^3 – 3. We know that dy/dx = 12x^3 - 24x^2 (+0).
JC
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