SOLUTION: Use the definition of the derivation to show that (d/dx)(cos x)= -sin x. You can use the following 3 facts: lim h->0 (sin h)/h =1 lim h->0 (cos h -1) / h = 0 cos(θ + )

Algebra ->  Test -> SOLUTION: Use the definition of the derivation to show that (d/dx)(cos x)= -sin x. You can use the following 3 facts: lim h->0 (sin h)/h =1 lim h->0 (cos h -1) / h = 0 cos(θ + )      Log On


   

Question 486705: Use the definition of the derivation to show that (d/dx)(cos x)= -sin x.
You can use the following 3 facts:
lim h->0 (sin h)/h =1
lim h->0 (cos h -1) / h = 0
cos(θ + )= cosθcos - sinθsin
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Use the definition of derivative using limits:





Applying our known facts, we can treat cos x and sin x as constants and say that the first limit collapses to zero, and the second limit collapses to -sin x. Hence,



We could also use L'Hopital's rule to evaluate the limits, but that assumes we already know the derivative of cos x, so we shouldn't use it right now.