Differentiation of a Function wrt Another Function and Higher Order derivative of a Function - Practice Questions & MCQ

Differentiation of a Function wrt another Function and Higher Order derivative of a Function

Suppose it is required to differentiate a function u = f(x) w.r.t. another function v = g(x).

Here, f(x) and g(x) are different functions, but the variable i.e. x is the same. 

To find du/dv or dv/du, we first differentiate both function f(x) and g(x) w.r.t. x separately and then put these values in the following formulae:

Higher Order Derivative of a Function

The derivative of a function is itself a function, so we can find the derivative of a derivative. The new function obtained by differentiating the derivative is called the second derivative. Furthermore, we can continue to take derivatives to obtain the third derivative, a fourth derivative, and so on. 

Collectively, these are referred to as higher-order derivatives. The notation for the higher-order derivatives of y = f(x) can be expressed in any of the following forms:

Note:

• It is interesting to note that the notation for    may be viewed as an attempt to express more compactly.
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