Find dx/dt at 1

Question

Find  at  if  and .

Answer 1

This is an implicit differentiation problem. That is, we will assume (implicitly) that both x and y are functions of t, and differentiate the given equations with respect to t, using the chain rule:

According to the chain rule, df(y)/dt=df(y)/dy*dy/dt and df(x)/dt=df(x)/dx*dx/dt.

Thus for y=5x²+5 --> dy/dt=2x*dx/dt.

Use the original equation to find y(1) and then plug in the given values of x, y, and dy/dt and solve for dx/dt.

See? Easy. :-)

Answer 2

The best way to do this problem is to calculuate dy/dx. You can then use the formula dy/dt = dy/dx * dx dt to solve for dx/dt.