What is the derivative of y = 64*(x - 8)^2*sin x*cos x

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The derivative of `y = 64*(x - 8)^2*sin x*cos x` has to be determined. Use the product rule to find the derivative.

y' = `64*((x - 8)^2)'*sin x*cos x` + `64*(x - 8)^2*(sin x)'*cos x` + `64*(x - 8)^2*sin x*(cos x)'`

=> `64*2*(x - 8)*sin x*cos x` + `64*(x - 8)^2*cos x*cos x` + `64*(x - 8)^2*sin x*(-sin x)`

=> `64*2*(x - 8)*sin x*cos x` + `64*(x - 8)^2*cos^2 x` - `64*(x - 8)^2*sin^2`

=> `64*(x - 8)*sin 2x + 64*(x - 8)^2*cos 2x`

The derivative of `y = 64*(x - 8)^2*sin x*cos x` is `y' = 64*(x - 8)*sin 2x + 64*(x - 8)^2*cos 2x`

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