Find dy/dx. x = t sin(t), y = t² + 9t

Solution:

Given functions are the parametric functions.

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

x = t sin(t)

y = t² + 9t

dy/dt = 2t + 9

dx/dt = sin(t)dt/dt + td(sint)/dt

= sin(t) + tcost(t)

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

= (2t + 9)/(sin(t) + tcost(t))

Find dy/dx. x = t sin(t), y = t² + 9t

Summary:

dy/dx = (2t + 9)/(sin(t) + tcost(t)) if x = t sin(t), y = t² + 9t