SOLUTION: y=cos x ans.y'=-sin x i needed exact how to solve this problem

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Question 887580: y=cos x ans.y'=-sin x
i needed exact how to solve this problem
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
y = cosx
use definition of derivative
y' = d cos(x)/dx = limit as delta approaches 0 of ((cos(x+delta) - cosx) / delta)
now use the definition of cos (a +b)
y' = d cos(x)/dx = limit as delta approaches 0 of (cos(x)cos(delta)-sin(x)sin(delta)-cos(x) / delta) = limit as delta approaches 0 of [(cos(delta)-1/delta * cos(x)) - (sin(delta)/delta * sin(x)]
now use limits for sin and cos
y' = d cos(x)/dx = (0 * cos(x)) - (1 * sin(x) = -sin(x)