Question

if f(x)=(x³+6x²+12x-13)¹⁰⁰ find f’(x)?​

Answer 1

$300({x}^{2} + 4x +4)(x³+6x²+12x-13) ^{99}$

Step-by-step explanation:

$Given, \: \: f(x)=(x³+6x²+12x-13)¹⁰⁰ \\ Differentiating \: \: with \: \: respect \: \: to \: x, \\ f’(x) = 100(x³+6x²+12x-13) ^{100 - 1} \times (3 {x}^{3 - 1} + 2 \times 6x^{2 - 1} + 1 \times 12 {x}^{1 - 1} - 0) \\ = 100 (x³+6x²+12x-13) ^{99}(3 {x}^{2} + 12x +12)\\ = 100(3 {x}^{2} + 12x +12)(x³+6x²+12x-13) ^{99} \\ = 100 \times 3({x}^{2} + 4x +4)(x³+6x²+12x-13) ^{99} \\ = 300({x}^{2} + 4x +4)(x³+6x²+12x-13) ^{99}$