Question

consider the following function and express the relationship between a small change in x and the corresponding change in y in the form dy. f(x)

Answer 1

For the following function the relationship between x and corresponding change in y is expressed as dy = f'(x) dx.

As given in the question,

Function given to express the relation between x and y

y =f(x)

Differentiate both the side of function with respect to x to get small change in x and the corresponding change in y,

dy/dx = d/dx (f(x))

⇒ dy /dx = f'(x)

⇒dy = f'(x) dx

Therefore, for the following function the relationship between x and corresponding change in y is expressed as dy = f'(x) dx.

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