WebQuestions on Differentiation (With Answers) Here are a few solved questions based on differentiation concept. 1. Differentiate x5 with respect to x. Solution: Given, y = x 5 On differentiating w.r.t we get; dy/dx = d (x 5 )/dx y’ = 5x 5-1 = 5x 4 Therefore, d (x 5 )/dx = 5x 4 2. Differentiate 10x2 with respect to x. Solution: y = 10x 2 WebInitially there are 9 grams of the isotope present. a. Write the exponential function that relates the amount of substance remaining as a function of , measured in hours. b. Use a. to determine the rate at which the substance is decaying in hours. c. Use b. to determine the rate of decay at hours.
Calculus I - Derivatives of Trig Functions (Practice Problems)
WebHigher Order Derivatives. Derivatives of derivatives, such as 2nd and 3rd derivatives. Applications include acceleration and jerk. WebHigher Order Partials Consider the function f(x,y) =2x2 +4xy−7y2. We’ll start by computing the first order partial derivatives of f , with respect to x and y. fx(x,y) fy(x,y) =6x+4y =4x−14y We can then compute the second order partial derivatives fxx and fyy by differentiating with respect to x again, and with respect to y again. can i consume fish oil daily
Calculus I - Implicit Differentiation (Practice Problems)
WebThe higher order terms can be rewritten as − f ″ ( x j) h 2! − f ‴ ( x j) h 2 3! − ⋯ = h ( α + ϵ ( h)), where α is some constant, and ϵ ( h) is a function of h that goes to zero as h goes to 0. You can verify with some algebra that this is true. WebExamples on higher order derivative Problem 3: Find the 2nd order derivative if x = p (A – sin A) and y = p (1 – cos A) Solution: x = p (A – sin A) and y = p (1 – cos A) then ⇒ y’ (A) = dy/dA = p sin A ⇒ x’ (A) = dx/dA = p (1-cos A) ⇒ d y d x = p s i n A p ( 1 − c o s A) = 2 s i n A 2 c o s A 2 2 s i n 2 A 2 = c o s A 2 s i n 2 A 2 = c o t A 2 Now, WebThis booklet contains the worksheets for Math 1A, U.C. Berkeley’s calculus course. Christine Heitsch, David Kohel, and Julie Mitchell wrote worksheets used for Math 1AM and 1AW during the Fall 1996 semester. David Jones revised the material for the Fall 1997 semesters of Math 1AM and 1AW. can i contact barclaycard via email