Rules for Derivatives in Calculus

Derivative is the measure of the rate of change at any given point on a curve. The rate of change of a function is the slope of a line.
The derivative of f(x) when the limit extends from h to 0 is given by the formula:

Derivative Rules:  

Derivative Rule of a given function in calculus can be categorized as follows:

• General Derivative Rules, 

• Logarithm Functions Derivatives, 

• Exponential Functions Derivatives,

• Trignometric Functions Derivatives and

• Derivative Rules of Inverse Hyperbolic Functions

Derivative of a constant term:
1.       Derivative of a constant term:

   d/dx (c)=0

2.       Power Rule of Derivative:

 d/dx  x^n=  n x^(n-1)

3.       Derivative of a variable with respect to itself:  

            d/dx(x)=1

4.       Power Rule for Function:

      d/dx  [f(x)]^n=n [f(x)]^(n-1)  d/dx  f(x)

5.       Derivative of a square root:

      d/dx vx=1/(2vx)

6.       Derivative of a root of a function:

      d/dx  v(f(x) )=1/(2v(f(x) ))  d/dx  f(x)

                        =1/(2v(f(x) ))  f^' (x) 

7.       Derivative of a constant times a function:

      d/dx  c.f(x)=c  d/dx  f(x)= c .f^' (x) 

8.       Derivative of sum or difference of two functions:

      d/dx  [f(x)±g(x)]=d/dx  f(x)±d/dx  g(x)= f^' (x)± g^' (x)

9.       Chain Rule of derivatives:

      d/dx  [f(g(x))]=f^' g(x).g^' (x)

10.   Derivative Product Rule:

    d/dx [f(x)  .g(x)]=f(x)  d/dx  g(x)+ g(x)  d/dx  f(x)  

             = f(x) g’(x) + g(x) f’ (x)

11.   Derivative Quotient Rule:

d/dx  [f(x)/g(x) ]=[g(x)  d/dx  f(x)- f(x)  d/dx  g(x)]/[g(x)]²

            =  [ g(x) f^' (x)- f(x) g^' (x)]/ [g(x)]²

Derivative Rules of Logarithm Functions:

Derivative Rules of Exponential Functions:

Derivative Rules of Trignometic Functions:

Derivative of Inverse Hyperbolic Functions: