What is expand f'(x)(1-3x^2)^3 ?

The solution to expand f'(x)(1-3x^2)^3 is f'(x)-9x^2f'(x)+27x^4f'(x)-27x^6f'(x)

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expand f'(x)(1-3x^2)^3

expand

f^{'} (x) (1 - 3 x^{2})^{3}

f' (x) - 9 x^{2} f' (x) + 27 x^{4} f' (x) - 27 x^{6} f' (x)

Solution steps

f^{'} (x) (1 - 3 x^{2})^{3}

(1 - 3 x^{2})^{3} = 1 - 9 x^{2} + 27 x^{4} - 27 x^{6}

= f^{^{'}} (x) (- 27 x^{6} + 27 x^{4} - 9 x^{2} + 1)

Distribute parentheses

= f^{^{'}} (x) 1 + f^{^{'}} (x) (- 9 x^{2}) + f^{^{'}} (x) 27 x^{4} + f^{^{'}} (x) (- 27 x^{6})

Apply minus-plus rules

+ (- a) = - a

= 1 f^{^{'}} (x) - 9 x^{2} f^{^{'}} (x) + 27 x^{4} f^{^{'}} (x) - 27 x^{6} f^{^{'}} (x)

Multiply:

1 f^{'} (x) = f^{'} (x)

= f^{^{'}} (x) - 9 x^{2} f^{^{'}} (x) + 27 x^{4} f^{^{'}} (x) - 27 x^{6} f^{^{'}} (x)

\frac{d ^{2}}{d x ^{2}} ((y) (x + y))

- 32 (1 - 37) + \frac{- 16 - 272 37}{27}

(n + 2 i - n + i) n

3 (10 - 2)

(e - 4) (e - 2) (e + 8)

What is expand f'(x)(1-3x^2)^3 ?
The solution to expand f'(x)(1-3x^2)^3 is f'(x)-9x^2f'(x)+27x^4f'(x)-27x^6f'(x)