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

Answer 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))

Answer 2

take derivative with respect to t
=4(cos(x)dx/dt-xsin(x)dx/dt)
plug in 4xcosx for every dx/dt
=4(cos(x)(4xcosx)-xsin(x)(4xcosx))