How do you differentiate $f (x) = sin (3 x - 2) \cdot cos (3 x - 2)$ $f(x) =sin(3x-2)* cos(3x -2)$ ?

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How do you differentiate $f (x) = sin (3 x - 2) \cdot cos (3 x - 2)$ $f(x) =sin(3x-2)* cos(3x -2)$ ?

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Answer 1 · 2016-04-04T09:10:24

Remember that

$sin 2 A = 2 \cdot sin A \cdot cos A$ $sin2A=2*sinA*cosA$

Hence

$f (x) = sin (3 x - 2) \cdot cos (3 x - 2) \Rightarrow f (x) = \frac{1}{2} \cdot sin (2 \cdot (3 x - 2))$ $f(x)=sin(3x-2)*cos(3x-2)=>f(x)=1/2*sin(2*(3x-2))$

Hence

$\frac{d f}{d x} = \frac{1}{2} \cdot cos (2 (3 x - 2)) \cdot 6 = 3 \cdot cos (6 x - 4) =$ $(df)/dx=1/2*cos(2(3x-2))*6=3*cos(6x-4)=$

Finally

$f'(x)=3*cos(6x-4)$

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How do you differentiate $f (x) = sin (3 x - 2) \cdot cos (3 x - 2)$ $f(x) =sin(3x-2)* cos(3x -2)$ ?

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How do you differentiate $f (x) = sin (3 x - 2) \cdot cos (3 x - 2)$ $f(x) =sin(3x-2)* cos(3x -2)$ ?