derivatives of a parametric equation

derivatives of a parametric equation - Printable Version

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derivatives of a parametric equation - DrD - 07-22-2018 11:17 AM

Is there an hp prime command for finding derivatives of parametric equations, with respect to a parametric variable?

For example, find the second derivative of a parametric equation where:
x = t² - 4;
y = t³ - 3*t;

Result: d²y/dx² = (3*t²+3) / (4*t³);

-Dale-

RE: derivatives of a parametric equation - Aries - 07-22-2018 03:26 PM

https://education.ti.com/html/t3_free_courses/calculus89_online/mod23/mod23_lesson2.html Wink

Best,

Aries Smile

RE: derivatives of a parametric equation - parisse - 07-22-2018 04:58 PM

Code:

y1:=diff(y,t); x1:=diff(x,t); normal(diff(y1/x1,t)/x1);

Since x1=dx/dt and y1=dy/dt, dy/dx=y1/x1, then d2y/dx^2=d(dy/dx)/dx=d/dt(dy/dx)/x1

RE: derivatives of a parametric equation - Aries - 07-23-2018 09:15 AM

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Best,

Aries Wink

RE: derivatives of a parametric equation - DrD - 07-23-2018 09:25 AM

Thank you Parisse, (and Aries). I was looking for a single pre-existing command that would perform this operation, (in the toolbox catalog). I didn't find anything specifically, but there is always the chance I might have missed it!

-Dale-