Solve Product Rule and Quotient Rule Problems (Calculus Problems and Solutions)

In this video we solve calculus problems about the product rule and quotient rule, but avoiding the chain rule (that will be the next video). Many involve e^x as well. Infinite Powers, How Calculus Reveals the Secrets of the Universe: https://amzn.to/37PBMjb.

🔴 Calculus 1, Lesson 1.1: Linear Functions (3Blue1Brown SoME2): https://www.youtube.com/watch?v=lmCjnxzIals

🔴 Calculus 1, Lesson 1.2: Exponential Functions: https://www.youtube.com/watch?v=47ZqW19AjD4

🔴 Calculus 1, Lesson 1.3: Quadratic Functions, Transformations of Functions, and Function Composition: https://www.youtube.com/watch?v=1T58CnSME4g

🔴 Calculus 1, Lesson 1.4: Logarithmic Functions (Intro to Horizontal Compressions & Inverse Functions): https://www.youtube.com/watch?v=oS-gvIoJf60

🔴 Calculus 1, Lesson 1.5: Trigonometric Functions and Inverse Trigonometric Functions: https://www.youtube.com/watch?v=UFYjlnGUenE

🔴 AP Calculus AB Exam Review: Practice Exam Problems & Solutions (Multiple Choice, No Calculator): https://www.youtube.com/watch?v=2AG_Dt3x7q0

🔴 AP Calculus AB Exam Review: Free Response Practice Exam Problems & Solutions: https://www.youtube.com/watch?v=RLgUwP44V_M

🔴 AP Calculus BC Exam Review: Practice Exam (30 Question Multiple Choice, No Calculator): https://www.youtube.com/watch?v=1Q7ALcwT97A

🔴 AP Calculus BC Exam Review: Free Response Practice Exam Problems & Solutions: https://www.youtube.com/watch?v=ZWisJEDP44w

🔴 Calculus 1 Exam 1 Review Problems and Solutions (Precalculus, Limits, Continuity, Derivatives): https://www.youtube.com/watch?v=UjmvUwvd7c4

🔴 Calculus 1 Course, Lecture 1: The Big Ideas (Rates & Areas, the Infinity Principle & Circular Area): https://www.youtube.com/watch?v=2V_ehJC5QUY

🔴 Calculus 1 Course Lecture Playlist: https://www.youtube.com/playlist?list=PLmU0FIlJY-MkFrKtM0S0NLu-TxZa5jBIx

#ProductRule #QuotientRule #calculus

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(0:00) Derivative of e^(2x) with Product Rule (avoid chain rule at the moment)
(2:25) Derivative of e^(-x) with Quotient Rule (avoid chain rule at the moment)
(5:22) Derivative of (x^3+x*sqrt(x))*4^x (Product Rule, Power Rule, and Linearity of Derivatives)
(7:25) Derivative of (x^2+5x+3)/(x^2*e^(x)) (Quotient Rule, Product Rule, Power Rule, Linearity)
(9:37) Derivative of (f(x)*g(x))/h(x)
(10:56) First and second derivative of 2x*e^(-x)
(15:19) Equation of tangent line to 2x*e^(-x) at x=0
(16:24) Intervals where 2x*e^(-x) is decreasing
(19:01) Intervals where 2x*e^(-x) is concave up
(21:02) Antiderivative based on Product Rule
(22:58) Antiderivative based on Quotient Rule
(24:16) Revenue derivative with respect to price (based on demand derivative with respect to price and the Product Rule)
(34:58) Fuel efficiency derivative with respect to speed (gas mileage)

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