respect to a function

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..

Derivative of a Function of a Function - So far, we know how to differentiate functions like sin x and x 3 - 5. But how do we differentiate a function of a function? That is how can we differentiate sin (x 3 - 5)?So far, we know how to differentiate..

The differentiation of function of a function is known as 'chain rule'. The chain rule is probably the most widely used differentiation rule in mathematics. If y is a differentiable function of u and u is a differentiable function of x, then the d..

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..

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. For ready re..

Orbital Wave Functions and Shapes of Orbitals - According to wave mechanics, orbitals are described by wave functions known as orbital wave functions. These orbital wave functions can be represented as a product of two functions: (i) Radial wave ..

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..

Replacement of hydroxyl group in carboxylic acids with a halogen, carboxylate, alkoxy or amino group gives functional derivatives of carboxylic acid known as acyl halides, acid anhydrides, esters or amides respectively..

Summary - The biotic and abiotic components form an interacting system called 'ecosystem'. Producers, consumers and decomposers are the various trophic levels, which are linked by their food relationship forming a 'food chain'. Several food chains are interrelated and interconnected to form a netwo..

What are the values of x and y that minimize the objective function D = 7 x + 2 y subject to the constraints x ≥ 0, y ≥ 0, x ≤ 2 y + 1 and y ≤ 4 - x respectively? => x = 1, y = 0 or x = 0, y = 0 or x = 0, y = 1 or x = 0, y = 4..