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Chain Rule for Derivatives. Example Problem d/dx((3x^2 -5)^4)= We can take the derivative of 3x squared minus 5 all raised to the fourth power by applying the chain rule. The clue here that we're going to use the chain rule is the fact that this is not a nice polynomial function, it's not the product…

CFA Level 2 – Fixed Income, Session 15-Reading 58, Asset-Backed Sector of the Bond Market-LOS b (Notes, Practice Questions, Sample Questions)  1. Prepayment tranching refers to: A) subdividing a corporate bond so some components pay coupon and others pay principal.B) subdividing a corporate bond so some components pay earlier coupon payments than others.C) subdividing an asset or…

Closed and bounded regions The mathematical process of optimization involves finding the maximum or minimum value of a function over a region. If we want to find the maximum of a function of x on an interval and the function is differentiable on this interval, we will have two cases to consider. The maximum can…

Optimal Value of Measurements (Two Dimensions) Optimization is the process of finding values that make a given quantity the greatest (least) possible given certain conditions.Maximum – greatest possibleMinimum – least possibleExample 1 (Maximize Area Given Perimeter):a) Suppose you have 40 m of fencing. You want to make a rectangular dog pen. What is the maximum…

Quotient Rule for Derivatives The quotient rule is an important derivative application in calculus. It allows us to find the derivative of a quotient of two functions. The quotient rule S not a single equation but rather a collection of related rules that allow us to find derivatives of all kinds of expressions involving division….

Unit 2 Exponents and Algebra 1. Exponent Lawsa) Product Rule: xmxn=xm+nExamples: Simplify-2ab54a4b3=-24aa4b5b3=-8a1+4b5+3=-8a5b8b) Quoent Rule: xmxn=xm-nExamples: Simplifyx7y4x3y4=x7-3y4-4=x4y0=x4c) Power of a Power Rule: xmn=xmnExamples: Simplify2x2y73=23x23y73=8x23y73=8x6y21Some more exponent rules:xyzm=xmymzmxym=xmym,y0x0=1,×0 2. Distribuve Property: ab+c=ab+acExamples: Simplify-2x(3x+5)=-2x(3x)-2x(5)=-6×2-10×3. Simplifying expressions (Adding and Subtracng Polynomials)Examples: Simplify3(x + 5)-2(x-6)=3x + 35-2x-26 Distribute=3x+15-2x+12 Simplify (Multiply)=3x-2x+15+12 Collect Like Terms=x+27 Simplify (Add/Subtract)

IGCSE Coordinated Science: Extraction of metal 1 Describe the use of carbon in the extraction of some metals from their ores. In case of iron, the oxides are reduced by reaction with Carbon and/or Carbon Monoxide.  2 Describe the essential reactions in the extraction of iron in the blast furnace. Coke (Carbon), Haematite (Iron II…

IGCSE History: World War I – Technology Did Technology Help Break the Stalemate? Trench warfare technology had not evolved: Cavalry charges were used: 30th March 1914 one such charge ended in disaster with only 4/150 horses surviving the charge. Machine guns could stop these attacks with impunity. Horses and mules were still employed for transport….

IGCSE Coordinated Science: Thermal Capacity 1. Demonstrate understanding of the term thermal capacity Thermal Capacity is often defined to be the amount of thermal energy required to raise the temperature of a substance by 1 Kelvin. Obviously, different substances have different thermal capacities. 2. Describe an experiment to measure the specific heat capacity of a…

IB Chemistry: Spontaneity Spontaneity Introduction A spontaneous reaction is often defined as “a reaction that causes a system to move from a less stable to a more stable state”. This unit will focus on this idea of spontaneity, and how we can link the previous concepts of entropy and enthalpy to Spontaneity. Predict whether a…