What is the difference between Diffrentiation and Derivatives?

Hasan Ali, 12 years ago

Grade:12

3 Answers

Ashwin Sinha

520 Points

12 years ago

Dear Hasan Ali,

When you are dealing with functions of one variable, there is very little difference, at least superficially, i.e., between whatever is implied by the derivative and the concept of differentiation. However there is a difference, which does eventually emerge, the more that one explores the real meaning of these two terms. So some examples should suffice to make things clear.

Consider a function of one variable such as y = sin(x^2). If we wish to take the derivative, we most likely want to find dy/dx which would be y'= cose(x^2)*2x, where we have simply used the the known derivative of sin(u) and applied the chain rule accordingly.

Now let us consider a function like A = cos (b*x - omega*t). This equation is intended to imply a propagating wave function which is both a function of space, i.e., the x variable, and t, the time variable. The question "what is the derivative" is not so clear here; since it is clear that we could be talking about derivatives with respect to either the spatial position or with respect to time. So we proceed by first taking the "total differential"

dA = -sine(b*x-omega*t) * (b*dx - omega*dt)

We now if a choice - if we want only the derivative with respect to time then we would obtain:
dA/dt = -sine(b*x-omega*t)*(-omega),

whereas if we wanted dA/dA we would obtain:
dA/dx = -sine(b*x-omega*t)*b

In short - differentiation is the process of finding either differentials or derivatives. The derivative is the result of performing the process of differentiation with respect to usually only one variable at a time, although in some cases you will find so-called "mixed partials" which involve taking a first derivative with respect to one variable, and then a second derivative with respect to another.

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kaushal kirti

32 Points

12 years ago

Differentiation is just opposite of integration. in this we try to findd out the small increment or decrement of any thing. u may understand it well if u have solved mechanics in physics.in maths we us it for equation. derivatives are what we derive from any equation.

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