ஒரு புள்ளியில் வகையீடு வடிவியல் விளக்கம்
Geometrical Meaning of Derivative at a Point
Table of Contents
- ஒரு புள்ளியில் தொடுகோட்டின் சாய்வு
- Graphical Meaning of Derivative at a Point
- ஒரு புள்ளியில் வகைமை/வகைமையின்மை
- Differentiable/Not Differentiable at a Point
- ஒரு சார்பின் வகைக்கெழு
- Derivative of a Function
Graphical Meaning of Derivative at a Point
[math]y=-5x^2+7x[/math] எனும் வளைவரைக்கு [math]\left(5,f\left(5\right)\right)[/math] என்ற புள்ளியில் தொடுகோட்டின் சாய்வினைக் காண்க.
Q.No.1
[b][math](1,1)[/math][color=#ff0000] என்ற பு[code][/code]ள்ளியில் [/color][/b][math]y=\sqrt{x}[/math][b][color=#ff0000] என்ற வளைவரையின் தொடுகோட்டின் சாய்வு[/color][/b]
Q.No.2
[b][math](0,0)[/math][color=#ff0000] என்ற புள்ளியில்[/color][/b][math]y=sin\left(x\right)[/math] [color=#ff0000][b]என்ற வளைவரையின் தொடுகோட்டின் சாய்வு[/b][/color]
Q.No.3
[b][color=#ff0000][math]x=\pi[/math] என்ற புள்ளியில் [math]y=\frac{cosx}{1-sinx}[/math] என்ற வளைவரையின் தொடுகோட்டின் சாய்வு[/color][/b]
Differentiable/Not Differentiable at a Point
[math]x=0[/math][color=#ff0000][b] என்ற புள்ளியில்[/b][/color] [math]y=\left|x\right|[/math] [color=#ff0000][b]என்ற சார்பு வகைமையானதா?[/b][/color]
[math]x=\pi[/math] [color=#ff0000][b]என்ற புள்ளியில்[/b][/color] [math]y=sin\left(\left|x\right|\right)[/math] [color=#ff0000][b]என்ற சார்பின் தொடுகோட்டின் சமன்பாடு[/b] [/color]
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[/img]
Derivative of a Function
Q.No.1
[math]y=\frac{1}{x^3}[/math] [color=#ff0000][b]என்ற சார்பின் வகைக்கெழு [/b][/color]
Q.No.2
[math]y=sin\left(x\right)[/math] [color=#ff0000][b]என்ற சார்பின் வகைக்கெழு [/b][/color]
Q.No.3
[math]y=x-tan\left(x\right)[/math] [color=#ff0000][b]என்ற சார்பின் வகைக்கெழு [/b][/color]