Question

Differentiate 3x^4 (4-x)^3?

Answer 1

Given exprssion : d/dx [ 3X⁴(4 - x )³ ]

Apply formula : ( a - b )³ = a³ - b³ + 3ab² -  3a²b

d/dx [ 3X⁴ ( 4³ - x³ + 3(4)x² -  3(4²)x ) ]

d/dx [ 3X⁴ ( 64 - x³ + 12x² -  48x ) ]

d/dx [192X⁴ - 3x⁷ + 36x⁶ -  144X⁵ ]

Apply formula : d/dx [Xⁿ] = nX^n-1

192(3)X^4-1 - (3)(7)x^7-1 + 36(6)x^6-1 -  144(5)X^5-1

576X³ - 21x⁶ + 216x⁵ -  720X⁴

- 21x⁶ + 216x⁵ -  720X⁴ + 576X³

The Solution is : - 21x⁶ + 216x⁵ -  720X⁴ + 576X³