lim x->x0   (f(x0)-f(x))/(x0-x)
lim h->0	(f(x+h)-f(x))/(h)

x0=x+h


x^2

lim h->0 (f(x+h)-f(x))/(h)=
lim h->0  ((x+h)^2-x^2) / h =
lim h->0  (x^2+2xh+h^2-x^2) / h = 
lim h->0  (2xh+h^2)/h =
lim h->0  2x + h  = lim h->0 2x + lim h->0 h = 2x+0


tgx= sinx/cosx = (cosx*cosx + sinx*(sinx)) / cos^2(x) =
=1/cos^2x

f'(x)=(-5x^8 + 2/3*x^-2 + 1/5x -21)'= -5*8*x^7  + (-2)*2/3*x^-3 + 1/5 + 0

f'(x)=(6 x^(3/2) -3 x^3/2 - 6/5*x^-5 + 2*x^-2  )' = 
		(6*3/2*x^1/2 - 3 *3/2*x^1/2 - 6/5* x^-6 + 2*-2x^-3)

f'(x)= (-3* x^9/2 / x^3/2 ) ' =  -3  * (9/2*x^7/2*x^3/2 - 3/2x^1/2*x^9/2)/(x^6/2) = 
  = -3 (9/2*x^5 - 3/2*x^5)/x^3=-3 (3 x^5/x^3) = -9 x^2

f'(x)= (-3* x^6/2 ) ' = -9*x^2 


f'(x) = (x^2/5 + 3x)*sinx = (2/5*x^-3/5+3)*sinx + (x^2/5 + 3x)*cos x

f'(x) = 2^x * 4*cosx = 4*( (2^x)'* cox - 2^x*sinx) = 4*((2^x *lnx)*cosx - 2^x* sin x)

f'(x) = (sin(x^4))'  = cos(x^4)*(4*x^3)

f'(x) = ((sin x)^4)' = 4* (sinx)^3*cosx


f'(x) = (e^(cos^3 x))' = (e^(cos^3 x)) * (cos^3 x)' =  (e^(cos^3 x)) * (3*cos^2 x * -sinx)