how to find the derivative of a fraction using the power rule 1K 199K views 10 years ago Calculus Derivatives In this video I go over a couple of example questions finding the derivative of functions with fractions in them using the power rule
Courses on Khan Academy are always 100 free Start practicing and saving your progress now khanacademy math old ap calculus ab ab derivati Power rule 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 If n is an integer then dfrac d dx left x n right nx n 1 product rule
how to find the derivative of a fraction using the power rule
how to find the derivative of a fraction using the power rule
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Discover how the power rule helps us find derivatives of functions like 1 x x or x By rewriting these functions as x where n is a negative or fractional exponent we can apply the power rule to calculate their derivatives with ease About Transcript Sal differentiates h x 5x 7 and evaluates the derivative at x 16 This can actually be done quite easily using the Power rule Questions Tips Thanks Want to join the conversation Log in Sort by Top Voted Faheem 8 years ago Why do you cube 16 1 4 8 votes Upvote Downvote Flag Matthew Ponce de Leon
We start with the derivative of a power function f x xn Here n is a number of any kind integer rational positive negative even irrational as in x We have already computed some simple examples so the formula should not be a complete surprise d dxxn nxn 1 It is not easy to show this is true for any n Transcript Let s dive into the power rule a handy tool for finding the derivative of x This rule simplifies the process of taking derivatives especially for polynomials by bringing the exponent out front and decrementing the power We explore examples with positive negative and fractional exponents
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Start Practising In this explainer we will learn how to use the power rule of derivatives and the derivative of a sum of functions to find the derivatives of polynomials and general power functions We begin by recalling the definition of 1 Answer Shwetank Mauria May 1 2018 We use quotient rule as described below to differentiate algebraic fractions or any other function written as quotient or fraction of two functions or expressions Explanation When we are given a
Using this rule we can take a function written with a root and find its derivative using the power rule Example Find the derivative of the function y 4 sqrt x 6 sqrt 3 x 2 Solution First rewrite the function using algebra y 4 sqrt x 6 sqrt 3 x 2 4x frac 1 2 6x frac 2 3 Now apply the power rule Here we use the known power rule for y x2 y x 2 to find the derivative of its inverse function y x x1 2 y x x 1 2 This general idea recurs in later chapters when we introduce new functions and their inverses Example 9 7 Derivative of x x Consider the function y x x1 2 y x x 1 2
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how to find the derivative of a fraction using the power rule - We start with the derivative of a power function f x xn Here n is a number of any kind integer rational positive negative even irrational as in x We have already computed some simple examples so the formula should not be a complete surprise d dxxn nxn 1 It is not easy to show this is true for any n