y = sin³( $\pi$ - 9$\theta$ ). Find dy/d$\theta$ . A) - 27 cos( $\pi$ - 9$\theta$ ) sin²( $\pi$ - 9$\theta$ ) B) - 27 cos( $\pi$ + 9$\theta$ ) sin²( $\pi$ + 9$\theta$ ) C) - 27 cos ²( $\pi$ - 9$\theta$ ) sin( $\pi$ - 9$\theta$ ) D) - cos( $\pi$ - 9$\theta$ ) sin²( $\pi$ - 9$\theta$ ) E) - 27 sin²( $\pi$ - 9$\theta$ )

Question

Quizplus · Accepted Answer

We start by applying the chain rule to y with respect to F1F1F1S1F1F1F10: dy/dF1F1F1S1F1F1F10 = (dy/dx) * (dx/dF1F1F1S1F1F1F10) Where x = (F1F1F1S1F1F1F10 - 9F1F1F1S1F1F1F10) To find (dy/dx), we use the chain rule again, this time with respect to x: (dy/dx) = cos(x) * (d/dF1F1F1S1F1F1F10) [sin³(x)] Taking the derivative of x with respect to F1F1F1S1F1F1F10 gives us: (dx/dF1F1F1S1F1F1F10) = -9F1F1F1S1cos(F1F1F1S1F1F1F10 - 9F1F1F1S1F1F1F10) Putting it all together, we get: dy/dF1F1F1S1F1F1F10 = -9F1F1F1S1cos(F1F1F1S1F1F1F10 - 9F1F1F1S1F1F1F10) * cos(F1F1F1S1F1F1F10 - 9F1F1F1S1F1F1F10) * sin²(F1F1F1S1F1F1F10 - 9F1F1F1S1F1F1F10) Simplifying the expression, we get: dy/dF1F1F1S1F1F1F10 = -27cos(F1F1F1S1F1F1F10 - 9F1F1F1S1F1F1F10)sin²(F1F1F1S1F1F1F10 - 9F1F1F1S1F1F1F10) Therefore, the correct choice is A.

Y = Sin3 π\piπ - 9 θ\thetaθ ) Find Dy/d θ\thetaθ A) - 27 Cos

Y = Sin³ $\pi$ - 9 $\theta$ ) Find Dy/d $\theta$
A) - 27 Cos