differentiate a variable with respect to a function

In this section we explained with examples how to form Differential Equation. Suppose a family of curves depending on one constant is given by F 1 : f (x, y, a)= 0 .(1) where a R is the parameter Differentiating (1) with respect to x, we have g (x, y, y', a) = 0 .(..

Derivative of Inverse Trignometric Functions - Before finding the differentiation of inverse trigonometric functions, recall how the inverse trigonometric functions are defined and what the domain and range of each inverse trigonometric function. Fo..

The derivative of the function f with respect to a variable x is the function f ' whose value at x is provided the limit exist..

. Thus, state of the system may be defined as its conditions of existence of the system when its macroscopic properties have definite values. When the state of a system changes its macroscopic properties also change and acquire new definite values. The macroscopic properties are properties which ar..

The amount spent by Chris on a birthday party is a function of number of his friends whom he invited. Which of the following is a dependent variable? => Chris′s age or number of members in Chris′s family or number of friends Chris invited or amount spent by Chris on ..

The cost of a taxi ride from Edd′s home to his office is a function of the number of miles between his home and office. Which of the following is the independent variable? => The driving time to the office or The cost of the taxi ride or The distance between Edd′s ho..

The circular functions are functions of an angle. They are important in the study of triangles and modeling periodic phenomena, among many other applications. Trigonometric functions are commonly defined as ratios of two sides of a right triangle containing the a..

Which of the following is correct for a function that is differentiable at a point x = 3 ? => left hand side derivative = right hand side derivative at x = 3 or left hand side derivative may not be equal to the right hand side derivative at x = 3 or f (3) does not exist or the h..

Derivative of Implicit Functions - Till now, the functions that we have discussed, are explicitly functions of x. We have defined y in terms of x. Suppose we have an equation f(x,y) = 0, which cannot be put in the form of y=f(x) to differentiate in the usual ..

Till now, the functions that we have discussed, are explicitly functions of x. We have defined y in terms of x. Suppose we have an equation f(x,y) = 0, which cannot be put in the form of y=f(x) to differentiate in the usual way, we can still differentiate..