Find dy/dx. x = t sin(t), y = t² + 2t

Solution:

A derivative is the rate of change of a quantity y with respect to another quantity x.

A derivative is also termed the differential coefficient of y with respect to x.

Differentiation is the process of finding the derivative of a function.

Given that:

x = t sin (t)

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

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

dy/dt = d(t²+2t)/dt

dy/dt = dt²/dt + 2 dt/dt

dy/dt = 2t + 2

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

dy/dx = (2t + 2) / [sin (t) + t cos (t)]

dy/dx = 2(t + 1) / [sin (t) + t cos (t)]

Find dy/dx. x = t sin(t), y = t² + 2t

Summary:

dy/dx = 2(t + 1)/[sin (t) + t cos (t)] when x = t sin (t), y = t² + 2t