Question

como deribar f(x)=x²(x-2)⁴

Answer 1

${y=x^2(x-2)^4}\\{ \frac{dy}{dx} = \frac{dx}{dy} [x^2(x-2)^4]}\\{ \frac{dy}{dx} =x^2 \frac{dx}{dy}(x-2)^4 +(x-2)^4 \frac{dx}{dy} (x^2)}\\{\frac{dy}{dx}=x^2[4(x-2)^3 \frac{dx}{dy} (x-2)]+(x-2)^4(2x)}\\{\frac{dy}{dx}=4x^2(x-2)^3[ \frac{dx}{xy} (x)- \frac{dx}{dy} (2)]+2x(x-2)^4}\\\frac{dy}{dx}=4x^2(x^3-6x^2+12x-8)+2x(x^4-8x^3+24x^2-32x+16)}\\{ \frac{dx}{dy} =4x^5-24x^4+48x^3-32x^2+2x^5-16x^4+48x^3-64x^2+32x}\\{ \frac{dx}{dy} =6x^5-40x^4+96x^3-96x^2+32x}$