Product Rule for Differentiation
Product Rule for Differentiation - Let y = u. v, where both u and v are differentiable functions of x.Let y = u. v, where both u and v are differentiable functions of ..
Product Rule for Differentiation - Let y = u. v, where both u and v are differentiable functions of x.Let y = u. v, where both u and v are differentiable functions of ..Product Rule for Differentiation
Let y = u. v, where both u and v are differentiable functions of x.Let y = u. v, where both u and v are differentiable functions of x. or (u.v)' = u.v' + v .u' It can be remembered ..
Let y = u. v, where both u and v are differentiable functions of x.Let y = u. v, where both u and v are differentiable functions of x. or (u.v)' = u.v' + v .u' It can be remembered ..Cross Product or Vector Product of Two Vectors
. To understand the direction of the vector , let us refer to the figure. Imagine rotating a right handed screw whose axis is perpendicular to the plane formed by a and b so as to twist it from a to b through the angle p between them. Then the direction of advance of the screw gives the direction of..
. To understand the direction of the vector , let us refer to the figure. Imagine rotating a right handed screw whose axis is perpendicular to the plane formed by a and b so as to twist it from a to b through the angle p between them. Then the direction of advance of the screw gives the direction of..Rules for Writing Equilibrium Constant Expressions
Expression for the equilibrium constant of a reaction is written in the form of a ratio. The numerator consists of the molar concentration (or partial pressure) terms of the products each raised to a power equal to its stoichiometric coefficient in the balanced chemical equation, an..
Rules for Writing Equilibrium Constant Expressions
Rules for Writing Equilibrium Constant Expressions - Expression for the equilibrium constant of a reaction is written in the form of a ratio. The numerator consists of the molar concentration (or partial pressure) terms of the products each raised to a power equal to its stoichi..
Rules for Writing Equilibrium Constant Expressions - Expression for the equilibrium constant of a reaction is written in the form of a ratio. The numerator consists of the molar concentration (or partial pressure) terms of the products each raised to a power equal to its stoichi..Dot Product of Vectors and the Resolution of a Vector
It was mentioned earlier that, displacement vectors are added to displacement vectors, or velocity vectors are added to velocity vectors. Just as it is meaningless to add scalar quantities of different kinds, such as mass and temperature, so also it is meaningless to add vector quantities of diffe..
Example 2:
Differentiate the following function using product rule. y = (3 sec x - 4 cosec x) (2 sin x + 5 cos..
Function
We consider two sets A and B. We form the Cartesian Product, we form relations. From all the relations, we can select a few which satisfy the rule that each element of the set A is related to only one element of the set B. When a relation satisfies this rule, it is c..
Linear Algebra
Types of linear systems Gauss-Jordan elimination, Gauss-Jordan method Vectors and vector addition Geometrical solution sets of systems of equations Rectangular matrices to row echelon form Matrix multiplication Inverse to a square matrix Determinants of 2 by 2 and 3 by 3 matrices Row redu..
Biological diversity and maintenance of stability
The numerical strength and biomass of organisms affect the functioning of ecosystem. In ecosystems, the biotic communities usually contain a few common species represented by a large number of individuals or by a large biomass and a comparatively large number of individual species occurring in sma..
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