differentiate x^3-6x^2+2x=0

To differentiate an equation, the first step is multiplying the coefficients of the variables (the coefficient is the number a variable is already being multiplied by, for example in 6x the coefficient of the variable x is 6) by the number that variable is to the power of. For example, in x^3, the coefficient of x is 1, and x is to the power of 3, so to multiply the coefficient by the variable you would multiply 1 and 3, giving you 3. This number is the new coefficient, so x^3 becomes 3x^3The second step is to reduce the number the variable is to the power of by one. So, 3x^3 would become 3x^2.Applying these rules to the full equation:x^3 becomes 3x^2 (as already explained)-6x^2 becomes -12x (-6x2=-12 for the coefficient, 2-1 becomes 1 for the power)2x becomes 2 (2x1=2 for the coefficient, 1-0 becomes 0 for the power. As any value to the power of 0 equals the number 1, the x value is eliminated and becomes the number 1 multiplied by the coefficient which is just equal to the coefficient.)Therefore the fully differentiated equation becomes:3x^2-12x+2=0