F'(x)=((7x^6+8x^4+3x+10)*(8x^5+6x^3+3x+7)-(7x^6+8x^4+3x+10)*(8x^5+6x^3+3x+7)')/(8x^5+6x^3+3x+7)^2=((42x^5+32x^3+3)*(8x^5+6x^3+3x+7)-(7x^6+8x^4+3x+10)*(40x^4+18x^2+3))/(8x^5+6x^3+3x+7)^2=((33x^10+281x^8+318x^6+318x^5+96x^4+242x^3+9x+21)-(280x^10+446x^8+165x^6+120x^5+424x^4+54x^3+180x^2+9x+30))/(8x^5+6x^3+3x+7)^2=
-247x^10-165x^8+153x^6-198x^5-328x^4+188^3-180x^2-9)/(8x^5+6x^3+3x+7)^2
Если не ошиблась со знаками то,вроде, так