Question

f(x)=sin4x-cos4x f`(п/8)

Answer 1

f'(x)= cos4x*(4x)' - (-sin4x)*(4x)' = 4cos4x+4sin4x 

f'(p/8)=  4cos p/2 + 4sin p/2= 4*0+4*1=0+4=4

Answer 2

Подставляем значение x=П/8

sin(4*П/8)+cos(4*П/8)=sinП/2+cosП/2=1+0=1
Ответ:f(П/8)=1

Answer 3

To find the derivative of f(x), we use the chain rule and the derivative of sin(x) and cos(x):

f'(x) = cos(4x) * 4 - sin(4x) * 4

At x = π/8 (or 45 degrees in radians), we have:

f'(π/8) = cos(4π/8) * 4 - sin(4π/8) * 4

f'(π/8) = cos(π/2) * 4 - sin(π/2) * 4

f'(π/8) = 0 * 4 - 1 * 4

f'(π/8) = -4

Therefore, f'(π/8) = -4.