Finding a derivative using the quotient rule ( I keep getting different answers)

Question

Find dw/dx for w=(3x⁵+2x⁴-6x²)/x²

I have done this derivative a couple different times and I can't figure out what is right or wrong because it seems like I am using all the rules right and everything. 

1st attempt)

x^-2x [(15x³+8x²-12)+(-2x^-1)(3x⁴+2x³-6x)]

 

2nd)

(15x⁶+8x⁵-12x³-2x⁶+2x⁵-6x³)/x⁴

What am I doing wrong? 

Answer 1

You don't need the quotient rule for this one.  Just divide each term of the numerator by the denominator first, then differentiate term by term.  

y = (3x⁵+2x⁴-6x²)/x² = 3x⁵/x² + 2x⁴/x² - 6x²/x²

 

                              = 3x³ + 2x² - 6

 

So, y' = 9x² + 4x - 0 = 9x² + 4x

Answer 2

If       w = f/g      then

 

dw/dx = (f'g - fg') / g²     ---->  quotient rule

 

 

dw/dx = [(15x⁴ + 8x³ - 12x)(x²) - (3x⁵ + 2x⁴ - 6x²)(2x)] / x⁴

 

 

Now that I've set up the derivative, all you have to do is use algebra to simplify.