Do we always use Implicit differentiation in related rates ? Thank you in advance for the answer :)

Question

primeralph · Answer

It depends on the problem.

anonymous · Answer

What would be the best way to know when to use it ?

primeralph · Answer

The kind of problem.
If variable are mixed, it's most probably implicit, unless you know partial differentiation.

anonymous · Answer

i don't know partial differentiation yet, so i'll go with the variables

anonymous · Answer

when you say mixed, what do you mean exactly ?

primeralph · Answer

When there are more than one possible variable to differentiate with respect to.
For example: the equation of a circle has A as a function of only r, so dA/dr has only one way of happening. No need for implicit.
For a cylinder, the volume depends on radius and height, so dV/dr has to be implicit because there are two variables involved.

anonymous · Answer

what would you say for a Pythagorean triangle equation ?

primeralph · Answer

With respect to?

anonymous · Answer

the hypotenuse ?

primeralph · Answer

If all three variables are varying, then implicit is what to use.

anonymous · Answer

ok yeah,  it's the car going west second car going sounth problem with their velocities

anonymous · Answer

so the 3 variables would be varying

anonymous · Answer

thank you very much :)

primeralph · Answer

Be careful though. Sometimes the questions are really simplified so you don't need to use implicit. It really depends on the problem.

anonymous · Answer

ok, i will be careful ,  thank you very much :)