Last Updated: November 21, 2025
Common Derivatives
| Function | Derivative |
|---|---|
f(x) = c
|
f'(x) = 0 |
f(x) = x
|
f'(x) = 1 |
f(x) = xⁿ
|
f'(x) = nxⁿ⁻¹ |
f(x) = eˣ
|
f'(x) = eˣ |
f(x) = ln(x)
|
f'(x) = 1/x |
f(x) = sin(x)
|
f'(x) = cos(x) |
f(x) = cos(x)
|
f'(x) = -sin(x) |
Derivative Rules
| Rule | Formula |
|---|---|
Power Rule
|
d/dx[xⁿ] = nxⁿ⁻¹ |
Product Rule
|
d/dx[uv] = u'v + uv' |
Quotient Rule
|
d/dx[u/v] = (u'v - uv')/v² |
Chain Rule
|
d/dx[f(g(x))] = f'(g(x))g'(x) |
Common Integrals
| Function | Integral |
|---|---|
∫ k dx
|
kx + C |
∫ xⁿ dx
|
xⁿ⁺¹/(n+1) + C |
∫ 1/x dx
|
ln|x| + C |
∫ eˣ dx
|
eˣ + C |
∫ sin(x) dx
|
-cos(x) + C |
∫ cos(x) dx
|
sin(x) + C |
💡 Pro Tip:
Don't forget the constant of integration (+C) for indefinite integrals!