Find dy/dx. x = t sin(t), y = t² + 3t

solution:

Given functions are the parametric functions.

We know that differentiation of parametric functions is given by: dy/dx = dy/dt . dt/dx

Given:

x = tsin(t)

y = t² + 3t

dy/dt = 2t + 3

dx/dt = dtsin(t)/dt

= tdsint/dt + sint(dt)/dt

= tcost + sint

dy/dx = (dy/dt)/(dx/dt)

= (2t + 3) /(tcost + sint)

Find dy/dx. x = t sin(t), y = t² + 3t

summary:

dy/dx = (2t + 3) /(tcost + sint), when x = t sin(t), y = t² + 3t