To find the derivative of sinx with respect to x, we use the following formula:
d/dx (sinx) = cosx
Therefore, the derivative of sinx is equal to cosx.
We can also use the first principles approach to derive the same result:
lim h→0 [sin(x + h) – sinx]/h
= lim h→0 [sinxcos(h) + cosxsin(h) – sinx]/h
= lim h→0 [cos(h)] [sinx/h + (cosx – 1)]
= cosx
Using either method, we can conclude that the derivative of sinx with respect to x is equal to cosx.
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