Question

Determine if the statement is always true, sometimes true, or never true.

If y is a function of x, and is also a function of t. then dy/dx = dy/dt

explain.

i think its sometimes true but i don't know why it is. am i right?, and can you please explain me y this is the case? Thank you for your time

Answer 1

it could be true, if x=t



But it would be a rare case...

for instance, x= t^2
y= x^3
dy/dx= 3x^2

y= x^3=t^6
dy/dt=6t^5=6x^2 sqrtx

so in general, dy/dx does not = dy/dt

it x=t, it will work out.
dy/dx=1=dy/dt