Derivatives

Here are the formulas you should remember about derivation:

Considering c a constant real number and a function defined as f(x) = c

f'(x) = 0

Considering c a constant real number and a function defined as cf(x)

cf'(x) = c(dy/dx)

Considering two constants c and d and considering two function cf(x) and dg(x). The derivative of 

(cf(x) + dg(x))' = cf'(x) + dg'(x)

Considering c a constant real number and a function defined as f(x) = cx

f'(x) = c

Considering a function in the form f(x) = ax + b

f'(x) = a.

Considering a function in the form f(x) = xn 

f'(x) = nxn-1

Considering a function in the form f(x) = ax2 + bx + c

f'(x) = 2ax + b

Considering u a function, considering that du/dx is its derivative, and considering u elevated to the power of n as in un 

f'(u) = nun-1du/dx

Considering u a function considering that du/dx is the derivative of that function, consider f(u)

f'(u) = (u')du/dx

Considering the product of two functions uv

(uv)' = u'v + uv'

 


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