Find derivative of cosx at x=0

Question

Using the formula, derivative of f at point a is denoted by f'(a), f'(a)=Lim(h→0) (f(a+h)-f(a)) /h

Answer 1

Derivative of cos(x) is (-1 times sin(x))

 

Since sin(0) = 0, the derivative of cos at x=0 is also 0 (zero can be neither positive nor negative; it is unsigned)

 

You can also look at the graph of y=cos(x) and see that at x=0, the tangent line is flat (parallel to the x-axis) which means that the slope of the curve is zero

Answer 2

f(x) = cosx

 

f'(a) = lim_h→0[(cos(a+h) - cosa)/h]

 

If a = 0, we have f'(0) = lim_h→0[(cosh - cos0)/h]

 

                                 = lim_h→0[(cosh - 1) / h]

 

                                 = 0   (A known limit that was probably discussed in class)