So, there are two pieces: the \(3x + 1\) (the inside function) and taking that to the 5th power (the outside function). Therefore, the derivative of each is zero. First, remember that integrals can be broken up over addition/subtraction and multiplication by constants. But, be careful at paying attention to the different forms a constant may take, as professors and teachers love checking if you notice things like that. Be sure to always check for this. Concavity of Graphs of Quadratic Functions, Differential Equations - Runge Kutta Method, Definition of the Derivative of a Function, Definition of Definite Integrals - Riemann Sums, Integral Form of the Definition of Natural Logarithm ln(x), Maximum Area of Rectangle - Problem with Solution, Maximum Radius of Circle - Problem with Solution, Find The Area of a Circle Using Integrals in Calculus, Find The Area of an Ellipse Using Calculus, Find The Volume of a Frustum Using Calculus, Find The Volume of a Square Pyramid Using Integrals, Maximum Area of Triangle - Problem with Solution, Maximum Area of Rectangle in a Right Triangle - Problem with Solution, Use Derivative to Find Quadratic Function, Use First Derivative to Minimize Area of Pyramid, Solve Rate of Change Problems in Calculus, Use Derivatives to solve problems: Distance-time Optimization, Use Derivatives to solve problems: Area Optimization, Minimum, Maximum, First and Second Derivatives, First, Second Derivatives and Graphs Of Functions, Calculus Questions, Answers and Solutions, Continuity Theorems and Their use in Calculus, Calculate Limits of Trigonometric Functions, L'hopital's Rule And The Indeterminate forms 0 / 0, Find Derivatives of Functions in Calculus, Rules of Differentiation of Functions in Calculus, Use the Chain Rule of Differentiation in Calculus, Derivative of Inverse Trigonometric Functions, Find Derivative of f(x) = arccos(cos(x)) and graph it, Find Derivative of f(x) = arcsin(sin(x)) and graph it, Find Derivative of f(x) = arctan(tan(x)) and graph it, Differentiation of Trigonometric Functions, Newton's Method to Find Zeros of a Function, Derivative, Maximum, Minimum of Quadratic Functions, Determine the Concavity of Quadratic Functions, Use Derivative to Show That arcsin(x) + arccos(x) = pi/2, Evaluate Integrals Involving Quadratics Using Completing Square, Integrals Involving sin(x) or cos(x) and Exponential, Integrals Involving sin(x) and cos(x) with odd power, Integrals Involving sin(x) with odd power, Integrals Involving sin(x) with even power, Evaluate Integrals Involving Logarithms - Tutorial, Evaluate Integrals Involving Logarithms - tutorial, Fourier Transform of Rectangular Functions, Order and Linearity of Differential Equations, Second Order Differential Equations - Generalities, Solve Second Order Differential Equations - part 1, Solve Second Order Differential Equations - part 2, Solve Second Order Differential Equations - part 3, Critical Points of Functions of Two Variables, Maxima and Minima of Functions of Two Variables, Optimization Problems with Functions of Two Variables, Second Order Partial Derivatives in Calculus. Find the derivative of the function: Head over this way to see the answer and more! Find the derivative of the function. We will write out every step here so that you can see the process. Differentiating each side using implicit differentiation, we get the following solution. In the example above, remember that the derivative of a constant is zero. As you can see, with product rule problems, you are really just changing the derivative question into two simpler questions. Both cars X and Y are headed for the intersection of the two roads.
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