differentiate a variable with respect to a function

The different ways of solving differential equation are a follows: (a). Method of separation of variables, (b). Homogeneous differential equations, (c). Linear differential equation..

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. For ready reference, the domain and range of these fun..

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..

State of the System and State Functions - State of the system implies the conditions of its existence. In order to understand it, let H 2 O be considered as a chemical system. H 2 O can exist in three physical states; ice, water and steam depending upon the conditions of temperature and p..

The expression, which when multiplied to a non-exact differential equation to convert it into exact differential equation is known as => A variable or A derivative or A factor or An integrating factor..

Choose a polynomial function in standard form with real coefficients whose zeros are 2 and - 6 and multiplicity of 3 and 2 respectively. => f(x ) = x 5 + 8 0 x 2 or f(x ) = - 24 x 3 + 8 0 x 2 or f(x ) = x 5 + 6 x 4 + 3 3 6 x - 2 8 8 or f(x ) = x 5 + 6 x 4 - 2 4 x 3 - 8 0 x 2 + 3..

The Objective Function is a linear function of variables which is to be optimised i.e., maximised or minimised. e.g., profit function, cost function etc. The objective function may be expressed as a linear expressio..

Definition - The figure is a unit circle, with origin O as centre cuts the x-axis at A (1,0) and let a variable point moving on the circumference move through an arc length q . i.e., AP = p( q ). The coordinates at the position of p( q ) are p(x,y) = (cos q , sin q ). Then the tangent ..

(1) Let the given function be f (x) on the real number line R. (2) Differentiate the function f(x) with respect to x and equate it to zero i.e., put f '(x) = 0. Solve for x. These values of x which satisfy f '(x) = 0 are called Critical values of the fu..

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 the..