MATH 105 Lecture Notes - Lecture 24: Product Rule, Pythagorean Theorem
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If y is written in terms of x, i. e. , y = f(x), then this is easy to do using the chain rule: . y = dy/dt = dy/dx dx/dt = dy/dx x. That is, find the derivative of f(x), plug in the value of x at the instant in question, and multiply by the given value of x = dx/dt to get y = dy/dt. There are two solutions to this problem: this is the simple way, just solve for y to get the function in the form that we"re used to dealing with and then differentiate. y= 1/x y = (1/x 2 ) But this does not work everytime, hence solution 2. If we could solve for y then we will get y as a function of x. In other words, if we could solve for y (as we could in this case but won"t always be able to do) we get y = y(x).