sin'x = cos x
derivatives of trigonometric functions can be proven by use of the
definition of derivative and the trigonometric limits.
If f(x) = sinx, then
Now that d(sinx)/dx equals cosx has been proven, what does
d(sinx)/dx look like in graph? Is it the same as cosx?
The value of the derivative at any value of x can be estimated
by drawing the tangent at the point (x, f(x)) and estimate its slope.
For example, at the point of x equals 0, draw the tangent at this point
and estimate its slope to be around 1, so d(sinx)/dx = 1. Now plot the
1) on the graph of df/dx or f '. By repeating this procedure
at different points, the graph of f ' can be drawn and will
resemble a cosine curve. The correction of the graph is confirmed
by formula (1).