g(x)=(cosθsinθ)^4 what’s the differential

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g(x)=(cosθsinθ)^4 what’s the differential

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Nick 5 years 2021-07-23T18:57:04+00:00 1 Answers 32 views 0

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  1. Nem
    0
    2021-07-23T18:58:19+00:00
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    Answer:

    sin²2θ. (cos θ sin θ). cos 2θ

    Step-by-step explanation:

    finding g'(x)

    g'(x)

    • (x^n)’ = nx^(n -1)

    = 4 (cosθsinθ)³ . { cosθ. (sinθ)’ + sinθ. (cosθ)’ }

    • (cosθ)’ = – sinθ
    • (sinθ)’ = cosθ

    = 4 (cosθsinθ)³ { cosθ. cos θ + sinθ.(-sin θ)}

    = 4 (cosθsinθ)³{ cos²θ – sin²θ}

    • cos²θ – sin²θ = cos 2θ
    • 2sinθ cosθ = sin 2θ

    = (4 cosθ sinθ)². (cosθ sinθ). { cos²θ – sin²θ}

    = sin²2θ. (cos θ sin θ). cos 2θ

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