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could someone help me out with 14? i tried it and I get that it uses chain rule and second derivative but I’m so lost please help

could someone help me out with 14 i tried it and I get that it uses chain rule and second derivative but Im so lost please help class=

Respuesta :

Answer:

d

Step-by-step explanation:

[tex]\frac{d}{dt}[/tex] (sinpt) = pcospt

[tex]\frac{d}{dt}[/tex](cospt) = - psinpt

Then

y = mcospt - nsinpt

[tex]\frac{dy}{dt}[/tex] = - mpsinpt - npcospt

[tex]\frac{d^2y}{dt^2}[/tex] = - mp²cospt + np²sinpt ← factor out - p² from each term

     = - p²(mcospt - nsinpt) ← this is y

     = - p²y

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