![]() ![]() We used the limit definition of the derivative to develop formulas that allow us to find derivatives without resorting to the definition of the derivative. Determine where V (t) (4t2)(1 +5t2) V ( t) ( 4 t 2) ( 1 + 5 t 2) is increasing and decreasing.The derivative of the quotient of two functions is the derivative of the first function times the second function minus the derivative of the second function times the first function, all divided by the square of the second function.The derivative of a product of two functions is the derivative of the first function times the second function plus the derivative of the second function times the first function.The derivative of the difference of a function \(f\) and a function \(g\) is the same as the difference of the derivative of \(f\) and the derivative of \(g\).The derivative of the sum of a function \(f\) and a function \(g\) is the same as the sum of the derivative of \(f\) and the derivative of \(g\).3.4 Product and Quotient Rule 3. The derivative of a constant \(c\) multiplied by a function \(f\) is the same as the constant multiplied by the derivative. Here is a set of practice problems to accompany the Finding Absolute Extrema section of the Applications of Derivatives chapter of the notes for Paul Dawkins Calculus I course at Lamar University. Product and Quotient Rule In this section we will give two of the more important formulas for differentiating functions.The derivative of a power function is a function in which the power on \(x\) becomes the coefficient of the term and the power on \(x\) in the derivative decreases by 1.Worked example: Product rule with mixed implicit & explicit. The derivative of a constant function is zero. Course: AP®/College Calculus AB > Unit 2.Should you proceed with the current design for the grandstand, or should the grandstands be moved?.If a driver loses control as described in part 4, are the spectators safe?.What is the slope of the tangent line at this point? What if a driver loses control earlier than the physicists project? Suppose a driver loses control at the point (\(−2.5,0.625\)).Is this point safely to the right of the grandstand? Or are the spectators in danger? To determine whether the spectators are in danger in this scenario, find the \(x\)-coordinate of the point where the tangent line crosses the line \(y=2.8\). ![]()
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