Question

Differentiati
ng both side means in physics

Answer 1

Answer:

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Answer 2

Answer:

Differentiation, say, can be the method to find the derivative.

There are identities which govern the technical background.

For Example.

We know, Velocity = Change in Displacement/Change in Time.

In Physics, we express it as

v = ∆x/∆t or dx/dt

Since the Displacement is a Vector quantity, it has magnitude and direction.

We resolve this vector, and for now, we give it values with regards to time.

Let x = 2t² i^ + 4t j^ + 5t k^

v = dx/dt

Now, We substitute the displacement value

v = d(2t² i^ + 4t j^ + 5t k^) / dt

Using Distributive property of Differentiation

d/dx(a + b) = d/dx(a) + d/dx(b)

We have

v = d/dt ( 2t² i^ ) + d/dt ( 4t j^ ) + d/dt ( 5t k^ )

Using the identity, d/dx (k × x to the power n) = k d/dx (x raised to n) where k is a constant

v = 2i^ [ d/dx (t²) ] + 4j^ [ d/dx (t) ] + 5k^ [ d/dt (t) ]

Now, we need to remember 2 identities.

d/dx (x to the power n) = n×x to the power (n - 1)

d/dx ( x ) = 1

By application of these identities in v,

v = (2i^ × 2t) + (4j^ × 1) + (5k^ × 1)

= 4ti^ + 4j^ + 5k^

So, the vector of velocity has its resolution as

4ti^ + 4j^ + 5k^.

This is differentiation.

The above mentioned is just an Example.