Derivative of this function
y= -7x³ -8x² +6x +3

In general, the derivative of a single term  Ax^(n)  is  A n x^(n-1) .

And the derivative of a sum of many terms is the sum of the derivatives
of the individual terms.  

Using these two rules, the derivative (with respect to 'x') of the expression
in the question is . . .

            Y' = -21x² - 16x + 6