Note: Assuming the limit exists and is finite.
f '(x)
Df(x)
f(x)
The line y = f(a) + f '(a). ( x – a ) is tangent to the graph of f at (a, f(a) ) .
D( constant ) = 0
D( x^{n} ) = n.x ^{n1}
D( sin(x) ) = cos(x)
D( cos(x) ) = –sin(x)
D( x ) = +1 if x > 0, undefined if x = 0, –1 if x < 0
Standard Function  The Function  Its Derivative 

Constant  Any constant, c  0 
Straight Line  x  1 
ax, for a constant a  a  
Square  x^{2}  2x 
Square Root  √(x)  (½)x^{(½)} 
Exponential  e^{x}  e^{x} 
a^{x}  ln(a) (a^{x})  
Logarithms  ln(x) 
1
x

log_{a}(x) 
1
x ln(a)


Trigonometry  cos(x)  sin(x) 
tan(x)  cos(x)  
sin(x)  sec^{2}(x)  
Inverse Trigonometry  sin^{1}(x) 
1
√(1x^{2})

tan^{1}(x) 
1
(1+x^{2})


cos^{1}(x) 
1
√(1x^{2})

Credit: https://www.mathsisfun.com/calculus/derivativesrules.html