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 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:
=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 Trignometic Functions:
