Possible derivation:
d/dx(4 x^3+8 x^6)
Differentiate the sum term by term and factor out constants:
= 4 (d/dx(x^3))+8 (d/dx(x^6))
Use the power rule, d/dx(x^n) = n x^(n-1), where n = 3: d/dx(x^3) = 3 x^2:
= 8 (d/dx(x^6))+4 3 x^2
Simplify the expression:
= 12 x^2+8 (d/dx(x^6))
Use the power rule, d/dx(x^n) = n x^(n-1), where n = 6: d/dx(x^6) = 6 x^5:
= 12 x^2+8 6 x^5
Simplify the expression:
Answer: |= 12x^2 + 48x^5
