Question

using definition, find derivative of f(x) =cos x at x=0 and x=π/2​

Answer 1

Answer:

solved

Step-by-step explanation:

f(x) =cos x

f ' (x) = - sinx

f ' (0) = 0

f ' ( π/2​) = - 1

Answer 2

Step-by-step explanation:

f(x)=cos x

f(x+h)=cos (x+h)

f'(x)=Lt h→0 f(x+h)-f(x)

h

=Lt h→0 cos(x+h)-cos x

h

= Lt h→0 -sin(2x+h).cos h

2 2

2 h

2

= Lt h→0 -sin(2x+h) Lt h→0 cos h/2

2 h/2

= -sin (2x)

2

= -sin x

At x=0

- sin 0= O

At x=π/2

- sin π/2=-1