Difference between revisions of "ParametricDerivative Command"

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;ParametricDerivative[<Curve x=x(t), y=y(t)>]: Returns a new [[Curves|parametric curve]] given by ''(x(t), <math> \frac{y'(t)}{ x'(t)}</math>)''.
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;ParametricDerivative( <Curve> )
:{{example|1=<code>ParametricDerivative[Curve[2t, t², t, 0, 10]]</code> (the curve equates to function ''f(x)=<math> \frac{x²}{4}</math>)'' returns the parametric curve ''(x(t)=2t,y(t)=t)'' (which equates to the derivative of the function ''f'(x)=<math> \frac{x}{2}</math>). }}
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:Returns a new [[Curves|parametric curve]] given by ''<math> \left( x(t), \frac{y'(t)}{ x'(t)} \right) </math>''.
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:{{example|1=<code>ParametricDerivative(Curve(2t, t², t, 0, 10))</code> returns the parametric curve ''(x(t) = 2t, y(t) = t)''. The curve given as argument to the command is the function ''f(x) = <math> \frac{x²}{4}</math>'', and the result is the derivative of that function: ''f'(x) = <math> \frac{x}{2}</math>.}}

Latest revision as of 09:41, 9 October 2017


ParametricDerivative( <Curve> )
Returns a new parametric curve given by \left( x(t), \frac{y'(t)}{ x'(t)} \right) .
Example: ParametricDerivative(Curve(2t, t², t, 0, 10)) returns the parametric curve (x(t) = 2t, y(t) = t). The curve given as argument to the command is the function f(x) = \frac{x²}{4}, and the result is the derivative of that function: f'(x) = \frac{x}{2}.
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