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vishal singh Grade: 11
        

how to find derative of sinx^ by first principle method

6 years ago

Answers : (3)

SAGAR SINGH - IIT DELHI
879 Points
										

Dear vishal


We can approximate this value by taking a point somewhere near to P(x, f(x)), say Q(x + h, f(x + h)).



tangent delta



The value math formula is an approximation to the slope of the tangent which we require.


We can also write this slope as "change in y / change in x" or:



m = Dy/Dx



If we move Q closer and closer to P, the line PQ will get closer and closer to the tangent at P and so the slope of PQ gets closer to the slope that we want.



tangent tangent



If we let Q go all the way to touch P (i.e. h = 0), then we would have the exact slope of the tangent.


Now, math formula can be written:



math formula



So also, the slope PQ will be given by:



math formula



But we require the slope at P, so we let h → 0 (that is let h approach 0), then in effect, Q will approach P and math formula will approach the required slope.




Putting this together, we can write the slope of the tangent at P as:



math formula




This is called differentiation from first principles, (or the delta method). It gives the instantaneous rate of change of y with respect to x.


This is equivalent to the following (where before we were using h for Δx):



dy dx



You will also come across the following for delta method:



delta



 























































Please feel free to ask your queries here. We are all IITians and here to help you in your IIT JEE preparation.


All the best.


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Sagar Singh


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6 years ago
Neer Varshney
76 Points
										

limh->0 sin(x).


=limh->0sin(x+h)-sin(x).


=limh->0[sin(x)cos(h)+cos(x)sin(h)-sinx] / h.


=limh->0[sinx(cos(h)-1) +cos(x)sin(h)[/h.


=limh->0[Sinx(cos(h)-1)]/h + [cos(x)sin(h)]/h.


=0+cos(x). {(cosx-1)/x = 0. sinx/x=1}


=cos(x).

6 years ago
Abhishek Panhale
16 Points
										

sinx^ what???

6 years ago
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