find the fist and second derivative of 5th root x^4 (x-4)^2

Answer 1

y=(x^4(x-4)^2)^.2 = (x^4(x^2-8x+16))^.2 = (x^6 -32x^5 +16x^4)^.2

y'= .2(x^6 -32x^5 +16x^4)(6x^5 - 160x^4+ 64x^3) = 1st derivative

= .2x^6 - .64x^5 + .32x^4)(6x^5 -160x^4+64x^3)

= .2x^11 - 32x^10 + 12.8x^9- 3.84x^10 + 102.4x^9 -2048x^8 +96x^9 - 2560x^8 + 1024x^7

= .2x^11 -35.84x^10 + 185.2x^9 - 4608x^8 + 1024x^7

y" = y')' = 2nd derivative

=.22x^10 -358.4x^9 + 1666.8x^8 - 36864x^7 + 7168x^6

(no guarantee the above is error-free. too tedious arithmetic to avoid 1 or 2 errors here or there)