Derivatives of Composite and Implicit Functions
Derivatives of Composite and Implicit Functions: Overview
This Topic covers sub-topics such as Differentiation of Implicit Functions, Derivative of Inverse Function, Differentiation of Inverse Trigonometric Functions and, Chain Rule for Differentiation of Composite Functions
Important Questions on Derivatives of Composite and Implicit Functions
If then :

If the dependent variable y is changed to 'z' by the substitution y = tan z then the differential equation is changed to then find the value of k.

Let be a polynomial of degree such that . If the real number is such that can be expressed as where are relatively prime, then equals

Let and let be the inverse of . Find the value of where

Find the derivative with respect to of the function :
at

If , find the value of .

If find

If , then is

Which of the following solution is obtained when is differentiated with respect to x

, then what would be the value of

Find .

Let and be the inverse function of , then is equal to

Suppose, the function has the derivative at and derivative at , the derivative of the function at has the value , then the value of is equal to:

If , then is equal to

Differentiate the following w.r.t

The derivative of the function is

Differentiate w.r.t .

If then is

Differentiation of w.r.t. is

Differentiation of w.r.t. is
