i am currently studying this, can i help?
Differentiation
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i know about it.
Do you know the importance of differentiation ?If you know,you may set a question to have fun!
1)What's the definition of differentiation?
2)What's the application of differentiation?
3)a.Let x^2-xy+y^2=7.Find dy/dx.
b.Find the equation of the normal to the curve x^2-xy+y^2=7at the point(1,3).
1) and 2) The way to find out how fast a function runs... ´steepness´ i think is the best translation...
3) what? i can only only differentiate (and the other way round) with one variable x, two is too much for me!
Please tell the answer!
Dekker,good try!
1)The definition is the slope of tangent with respect to x.
2)Differentiation is widely applicable such as engineering,scientific research etc.Also,we can find the velocity and acceleration of the car by differentiation.
3)a.Differentiate both sides with respect to x,
2x-y-(x)dy/dx+(2y)dy/dx=0
dy/dx=(2x-y)/(x-2y)
b.dy/dx|(1,3)=1/5
Since the normal is perpendicular to the tangent.(i.e.normal x tangent=-1)
The equation of normal:y-3=-5(x-1)
5x+y-8=0
Who has learned the differentiation? Maybe we can discuss it here......