The Derivative of a Constant Function
The derivative of any constant is zero.
The Power Rule
The power rule is true for all real numbers n .
The Constant Multiple Rule
if c is a constant and f is a differentiable function.
When new funtions are formed from old functions by addition, subtraction, or multiplication by a constant, their derivatives can be calculated in terms of derivatives of the old functions. In particular, the Constant Multiple Rule formula says that the derivative of a constant times a function is the constant times the derivative of the function.
The Sum Rule
if f and g are both differentiable, then the derivative of a sum of functions is the sum of the derivatives.
The Difference Rule
if f and g are both differentiable, then the derivative of a difference of functions is the difference of the derivatives.
Definition of the Number e
The function f(x)=e^x is the one whose tangent line at (0.1) has a slope f'(0) that is exactly 1.
Derivative of the Natural Exponential Function e
The function f(x) = e^x has the property that it is its own derivative. The geometrical significance of this fact is that the slope of the tangent line to the curve y=e^x is equal to the y-coordinate of the point.