What is a Derivative? Deriving the Power Rule

After discussing differentiation at great length, it is time to connect this concept with the act of taking the derivative of a function. In actuality these mean the same thing, but using the power rule to take the derivative of a function is actually much simpler than all that business with limits and tangent lines! But it is important to know what the power rule is and where it comes from, so let's derive it together. This way, when you take the derivatives of functions, you'll know exactly what is really happening. Watch the whole Calculus playlist: http://bit.ly/ProfDaveCalculus Watch the whole Mathematics playlist: http://bit.ly/ProfDaveMath Classical Physics Tutorials: http://bit.ly/ProfDavePhysics1 Modern Physics Tutorials: http://bit.ly/ProfDavePhysics2 General Chemistry Tutorials: http://bit.ly/ProfDaveGenChem Organic Chemistry Tutorials: http://bit.ly/ProfDaveOrgChem Biochemistry Tutorials: http://bit.ly/ProfDaveBiochem Biology Tutorials: http://bit.ly/ProfDaveBio EMAIL► ProfessorDaveExplains@gmail.com PATREON► http://patreon.com/ProfessorDaveExplains Check out "Is This Wi-Fi Organic?", my book on disarming pseudoscience! Amazon: https://amzn.to/2HtNpVH Bookshop: https://bit.ly/39cKADM Barnes and Noble: https://bit.ly/3pUjmrn Book Depository: http://bit.ly/3aOVDlT Learn more about your ad choices. Visit megaphone.fm/adchoices