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Posts Tagged ‘derivative’

Derivatives – Logarithms

Friday, September 4th, 2009

How to Solve Derivatives with Logarithmic Functions

Description

This video covers the basic exponential and logarithmic functions, and then shows several sample problems. Many example problems of solving for natural logs are provided in the video. This video also shows the relationship between exponents and natural logs.

Overview

Derivatives with logarithms are rather easy to solve. The first of these is the regular exponent. The exponent is an exponential function, not a logarithmic function, but the two are related. The solution for an exponent, e^x, is:

d/dx (e^x) = e^x

Remember that the exponential solution only works when the variable x is the exponent, and to not use this when you should be using the power rule. The two look very similar and it is easy to mix them up. A problem using the power rule looks like x^2. A problem using the exponential rule looks like 2^x.

The next of these is a natural log. A natural log is a logarithm in its natural form. It is not necessary to understand natural logs to solve a derivative problem with natural logs. This should be a derivative that you have memorized. The natural log is solved like this:

d/dx [ln(x)] = 1 / x

In other words, to solve a natural log simply put one over whatever is inside the parenthesis. Remember that it may be necessary to use other rules with this rule.

Tags: Calculus, derivative, derivatives, differentiation, exponential, exponents, logarithmic, logarithms, logs, Math, natural logarithms, natural logs
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Derivatives – Chain Rule

Friday, September 4th, 2009

How to Solve Derivatives Using the Chain Rule

Description

This video provides an example problem of the chain rule used with several other rules of calculus. Steps are organized in an easy-to-follow manner.

Overview

The chain rule is a rule in calculus that can be used to solve derivatives. It is not a complicated rule, but can still be very confuding when first learning it. The chain rule states that:

d/dx [f(n)] = f’(n) * n’

In other words, the derivative of the outside of the equation is done, leaving the inside intact. Then the derivative of the inside is multiplied to it. The chain rule is used every time sine, cosine, tangent, cosecant, cotangent, and secant are in a problem, and normally when a logarithm (or natural log) is involved. It is sometimes easier to split a problem into two seperate parts before solving.

Example: sin(2x) –> d/dx [sin(x)] = cos(x), d/dx (2x) = 2

Therefore: d/dx sin(2x) = cos(2x) * 2

Tags: Calculus, chain, chain rule, derivative, derivatives, differentiation, Math, multiplication
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Derivatives – Quotient Rule

Friday, September 4th, 2009

How to Solve Derivatives Using the Quotient Rule

Description

This video goes over the quotient rule and how to use it. It provides many sample problems and shows how to solve derivatives with the quotient rule in conjunction with other derivative rules.

Overview

The quotient rule is a rule in calculus that can help you solve derivatives that are divided. The basic form of the quotient rule is:

d/dx (u / v) = [(v * u') - (u * v')] / (v^2)

This translates to be the the denominator times the derivative of the numerator, minus the numerator times the derivative of the denominator, all over the denominator squared. To remember the quotient rule, you can also use the phrase “low di-high minus high d-low, square the bottom and away we go”

Tags: Calculus, derivative, derivatives, differentiation, divide, division, Math, quotient, quotient rule
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Derivatives – Product Rule

Friday, September 4th, 2009

How to Solve Derivatives Using the Product Rule

Description

This video shows when to use the product rule, how to use the product rule, and why you should use the product rule. Not only does it give several sample problems but it explains the entire process of how the product rule actually works, and why it helps you find the right answer.

Overview

The product rule is a rule in calculus that allows you to solve derivatives that are multiplied. The basic form of the product rule is:

d/dx (u * v) = (u * v’) + (v * u’)

In other words, the solution is the first term mulitplied by the derivative of the second term, plus the second term multiplied by the derivative of the first term. It is often required to use the product rule in combination with several other rules.

Tags: Calculus, derivative, derivatives, differentiation, Math, multiplication, product, product rule
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Derivatives – Power Rule

Friday, September 4th, 2009

How to Solve Derivatives Using the Power Rule

Description

This video explains both the Power Rule and the Constant Rule in-depth, and illustrates the difference between different functions with power rules on a graph. It provides several example problems that could be solved using the power rule.

Overview

The Power Rule is a rule in calculus that allows you to solve derivatives. The Power Rule deals with exponents, or powers. The simple power rule states that:

d/dx (x^n) = nx^(n – 1)

In other words, the number of the exponent gets placed in front of x, and then the exponent gets subtracted by 1. An interesting thing about the Power Rule is the \”chain of command\”. The power rule will be easier to use if you memorize this:

d/dx (x^0) = 0

d/dx (x^1) = 1

d/dx (x^2) = 2x

d/dx (x^3) = 3x^2

Tags: Calculus, derivative, derivatives, differentiation, Math, power, power rule
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