wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Find the differential coefficient of sinx by first principle.

Open in App
Solution

Find the differential coefficient of sinx by first principle. Suppose that
f(x)=sinx
f(x+h)=sin(x+h)
f(x+h)f(x)=sin(x+h)sinx
f(x+h)f(x)h=sin(x+h)sinxh
limh0f(x+h)f(x)h=limh0sin(x+h)sinxh
ddxf(x)=limh0⎢ ⎢ ⎢ ⎢2cos(x+h2).sinh2h⎥ ⎥ ⎥ ⎥
ddxsinx=limh0cos(x+h2).limh0⎜ ⎜ ⎜sinh2h2⎟ ⎟ ⎟
=cos(x+0).limh20⎜ ⎜ ⎜sinh2h2⎟ ⎟ ⎟h0
h20
=cosx.1
ddxsinx=cosx.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Derivative of Standard Functions
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon