Derivative of two equations

[P-isabel]

I need help to find dy/dx of the two following:
x(t)=3cos(4t)
y(t)=5sin(3t)

I know that:

x(t)=3 cos(4t)
d/dt= -12sin(4t)

and
y(t)=5sin(3t)
d/dt =15cos(3t)

 

[Dr.Peterson]

Do you know that dy/dx = (dy/dt)/(dx/dt)? This is a version of the chain rule.

 

[P-isabel]

Do you know that dy/dx = (dy/dt)/(dx/dt)? This is a version of the chain rule.

So that means its--> 15cos(3t)/-12sin(4t)

 

[Dr.Peterson]

So that means its--> 15cos(3t)/-12sin(4t)

Yes, but write that more carefully, with parentheses, (15cos(3t))/(-12sin(4t)), and simplify it a bit (canceling a common factor). There's not much more you can do.