Find dy/dx. x = t sin(t), y = t² + 7t

Solution:

Given are the parametric functions.

x = t sin(t)

y = t² + 7t

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

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

= sin(t) + tcos(t)

dy/dt = d(t²) /dt + d(7t)/dt

= 2t + 7

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

= (2t + 7)/(sin(t) + tcos(t))

Find dy/dx. x = t sin(t), y = t² + 7t

Summary:

dy/dx = (2t + 7)/(sin(t) + tcos(t)) x = t sin(t), y = t² + 7t