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$f(x)$ is a continuous and differentiable function for all $x$. The power series for $f$ centered at $x = 0$ is given by:

$$f( x ) =2x-\cfrac{6{ x }^{ 3 }}{5}+\cfrac{9{ x }^{ 5 }}{50}-\cfrac{5{ x }^{ 7 }}{280}+\cdots $$

...find $f’(x)$.

A

$f’(x)={ x }^{ 2 }-\cfrac{{ 3x }^{ 4 }}{10}+\cfrac{{ 3x }^{ 6 }}{100}-\cfrac{{ x }^{ 8 }}{448}+\cdots $

B

$f’(x)={ x }^{ 2 }-\cfrac{{ 3x }^{ 4 }}{10}+\cfrac{{ 3x }^{ 6 }}{100}+\cfrac{{ x }^{ 8 }}{448}+\cdots $

C

$f’(x)={ 2 }-\cfrac{{ 18x }^{ 2 }}{5}-\cfrac{9x^4}{ 10}+\cfrac{x^6}{8}-\cdots $

D

$f’(x)={ 2 }-\cfrac{{ 18x }^{ 2 }}{5}+\cfrac{9x^4}{ 10}-\cfrac{x^6}{8}+\cdots $

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