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

The solution to expand f'(2)(x^2+1)^2 is x^4f'(2)+2x^2f'(2)+f'(2)

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expand f'(2)(x^2+1)^2

expand

f^{'} (2) (x^{2} + 1)^{2}

x^{4} f' (2) + 2 x^{2} f' (2) + f' (2)

Solution steps

f^{'} (2) (x^{2} + 1)^{2}

(x^{2} + 1)^{2} = x^{4} + 2 x^{2} + 1

= f^{^{'}} (2) (x^{4} + 2 x^{2} + 1)

Distribute parentheses

= f^{^{'}} (2) x^{4} + f^{^{'}} (2) 2 x^{2} + f^{^{'}} (2) 1

= x^{4} f^{^{'}} (2) + 2 x^{2} f^{^{'}} (2) + 1 f^{^{'}} (2)

Multiply:

1 f^{'} (2) = f^{'} (2)

= x^{4} f^{^{'}} (2) + 2 x^{2} f^{^{'}} (2) + f^{^{'}} (2)

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What is expand f'(2)(x^2+1)^2 ?
The solution to expand f'(2)(x^2+1)^2 is x^4f'(2)+2x^2f'(2)+f'(2)