Calculus

Find d^2x/dt^2 as a function of x if dx/dt=4xcosx.

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  1. d²x/dt²
    =d(dx/dt)/dt
    =d(4xcosx)/dt
    Use the product rule,
    :::d(uv)=udv+vdu:::
    =4(1*cos(x)+x(-sin(x)))
    =4(cos(x)-xsin(x))

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