If-f-x-sin-4-2x-Find-f-pi-12-

Question Number 207127 by hardmath last updated on 07/May/24

If f (x) = \sin^{4} 2 x

Find f^{^{'}} (\frac{π}{12}) = ?

Answered by Skabetix last updated on 07/May/24

f (x) = \sin^{4} (2 x)

\Leftrightarrow f^{'} (x) = 8 {s i n}^{3} (2 x) c o s (2 x)

f^{^{'}} (\frac{π}{12}) = 8 {s i n}^{3} (\frac{π}{6}) c o s (\frac{π}{6})

= 8 \times {(\frac{1}{2})}^{3} \times \frac{\sqrt{3}}{2}

= 1 \times \frac{\sqrt{3}}{2} = \frac{\sqrt{3}}{2}

Commented by hardmath last updated on 07/May/24

thank you dear ser

Answered by mathzup last updated on 08/May/24

f^{^{'}} (x) = 4 \times 2 c o s (2 x) {s i n}^{3} (2 x) \Rightarrow

f^{^{'}} (\frac{π}{12}) = 8 c o s (\frac{π}{6}) \times {s i n}^{3} (\frac{π}{6})

= 8 \times \frac{\sqrt{3}}{2} \times {(\frac{1}{2})}^{3} = \frac{\sqrt{3}}{2}

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