How to do Differentiation ???
- In this post we will discuss about differentiation and how to solve problem of differentiation easily,because i know that many people have problem to solve problem based on differentiation.in this post i don't want to go in detail about differentiation but i want to discuss methods to solve it.
- suppose function F(X) is given than derivative of function F(X) is given by d/dx( F(X) ).for more information regarding to definition and theory details visit this link of Wikipedia click here .
- Now here is some calculated formula for derivative,we can also prove that formula easily.but,I think it is not necessary to do so.
- d/dx (X) = 1
- d/dx (X^2) = 2X
- d/dx (X^n) = n(X^(n-1))
- d/dx (constant)= 0
- d/dx (constant*X) = constant*d/dx (X)
- d/dx (sinX) = cosX
- d/dx (cosX) = -sinX
- d/dx (tanX) = sec^2 (X)
- d/dx (cotX) = -cosec^2 (X)
- d/dx (secX) = secX.tanX
- d/dx (cosecX) = -cosecX.cotX
- d/dx (1/X) = log (X)
- Still there are another formulas for derivative for inverse of trigonometric function.just go through it.
- Now,here are some rules of differentiation .remember it very well.because it is very important.
- Rule differentiation for summation for two functions F(X) and G(X)
- Rule differentiation for subtraction for two functions F(X) and G(X)
d/dx ( F(X) - G(X) ) = d/dx (F(X)) - d/dx
(G(X))
- Rule differentiation for multiplication for two functions F(X) and G(X).
- Rule differentiation for division for two functions F(X) and G(X)
I think I have covered almost all formulas and rules of simple
first derivative.Now we calculate some sum to built up
confidence.
(1) calculate d/dx (1 + X + 2X +X^2)
→ By applying rule of summation to given
function we get,
d/dx (1) + d/dx (X) + d/dx(2X) + d/dx
(X^2)
= 0 + 1 + 2 + 2X
( from the list of formula)
=3+2X
Thats it !!! differentiation is very easy , let us take another
example.
(2) calculate d/dx ( X+2(X^2)+sin^2(X)+[(sinX)/X] )
→ By applying rule of summation to given function we get,
= d/dx (X) + d/dx (2X^2) + d/dx (sin^2(X)) + d/dx [(sinX)/X]
= 1 + 2(2X) + 2sinX*cosX + [(X(d/dx (sinX))) - ((sinX)*(d/dx (X)) )/X^2]
=1+4X+sin2X+[(XcosX+sinX) / X^2 ] (sin2X = 2sinX*cosX)
Like that we can calculate any example easily.main thing is remember formulas and practice. My next post will be on higher order differential equation.so,keep practising of first order differential equation and built up confidence and keep ready for second order differntial equation.
(2) calculate d/dx ( X+2(X^2)+sin^2(X)+[(sinX)/X] )
→ By applying rule of summation to given function we get,
= d/dx (X) + d/dx (2X^2) + d/dx (sin^2(X)) + d/dx [(sinX)/X]
= 1 + 2(2X) + 2sinX*cosX + [(X(d/dx (sinX))) - ((sinX)*(d/dx (X)) )/X^2]
=1+4X+sin2X+[(XcosX+sinX) / X^2 ] (sin2X = 2sinX*cosX)
Like that we can calculate any example easily.main thing is remember formulas and practice. My next post will be on higher order differential equation.so,keep practising of first order differential equation and built up confidence and keep ready for second order differntial equation.
Comments
Post a Comment