Calculus theory

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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

  • Calculus theory -

    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

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