derivative given x and y in terms of t

[rubing]

I am trying to find dy/dx given x and y in 2 different equations in terms of t.

x= ln(t+1) y = t²

According to the text book I am reading I believe this is an instance where one should use the following rule: dy/dx = (dy/dt ) / (dx/dt)

When I compute the derivative in this way I get the answer

2t / [ 1 / (t + 1)] = 2t ( t + 1)

This differs from the book's answer which is: 2t / (t+1)


So, it seems I am very close, but somehow still at odds with understanding the mechanics of this procedure. Any input greatly appreciated. THX!!!

 

[cordoba]

I agree with you. I think perhaps the answer is a typo in your book.

 

[pappus]

I am trying to find dy/dx given x and y in 2 different equations in terms of t.

x= ln(t+1) y = t²

According to the text book I am reading I believe this is an instance where one should use the following rule: dy/dx = (dy/dt ) / (dx/dt)

When I compute the derivative in this way I get the answer

2t / [ 1 / (t + 1)] = 2t ( t + 1) <--- your result is OK

This differs from the book's answer which is: 2t / (t+1) <--- this must be a typo


So, it seems I am very close, but somehow still at odds with understanding the mechanics of this procedure. Any input greatly appreciated. THX!!!

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