Flipped Math
Calculus AB/BC - Derivatives of cos(x), sin(x), e^x, and ln(x)
The shortcuts are not just for polynomial functions. Pupils learn the derivatives of the two basic trigonometric functions, cosine and sine. The video provides the derivatives for exponential and logarithmic functions. Learners work...
Khan Academy
Proof: d/dx(ln x)=1/x
Using the definition of a limit, various properties of logarithms, and a definition of e, Sal shows the proof of the derivative of ln x = 1/x. Note: The video titled "Proof of Derivatives of Ln(x) and e^x,Ó has a more straightforward...
Khan Academy
Proof: d/dx(e^x) = e6x
Using the derivative of ln x, the chain rule, and the definition of a limit, Sal shows proof that the derivative of ex = ex. Note: The video titled "Proof of Derivatives of Ln(x) and e^x,Ó clearly explains this proof.
Flipped Math
Solving Exponential Equations
Logarithms and exponents go together like multiplication and division. A video lesson demonstrates solving exponential equations both graphically and using logarithms. Supplemental materials give learners an option to practice what...
Krista King Math
Finding Half Life
When will half of the substance be gone? Using the exponential decay formula, the video finds the half-life of radium-226. The 29th installment in a 31-part series goes on to discuss that the calculations are the same independent of the...
Krista King Math
How to Use Logarithmic Differentiation to Find the Derivative
Use the natural logarithm to simplify differentiation. The 22nd resource in a series of 31 provides an example of a problem that would be best differentiated by using logarithms. The presenter takes the natural logarithm of both sides....
Krista King Math
Derivatives of Logarithms
It is only natural to take the derivative of a logarithmic function with a complex argument. The 21st installment in a series of 31 provides an example of taking the derivative of a natural logarithmic function. First simplifying the...
Krista King Math
Derivative of x^x
Use this trick to find the derivative of x raised to the x power. The video shows how to find a complicated derivative by rewriting the function using properties of logarithms. After rewriting the function, the derivative is simply...
Educreations
Natural Log Function-Integration
One of the strongest tools in integration is u-substitution, particularly when working with natural logs. In this step-by-step video presentation, a pleasant-voiced instructor walks through a number of integration problems. She...
Curated OER
What is a Natural Logarithm?
The instructor shows how logarithms of base e can be written as using the natural logarithm notation, abbreviated ln.
Curated OER
How Do You Convert From Exponential Form to Natural Logarithmic Form?
This video shows how to convert an equation in exponential form to logarithmic form. The example shown uses base e, and it is converted to an equation using a natural logarithm.