calculus 1 homework

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Mathematics

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it is basic homework all these questions should be answered in full answer. include all steps

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Math 121 Summer 2018 May 23, 2018 Name: Writing Assignment 2 (Due Tuesday, May 29) 1. (a) State the definition of “the derivative of f (x) at x”. (b) Use the definition of derivative to determine the derivative of f (x) = 3x2 − 5x. (c) Use the definition of derivative to determine the derivative of √ f (x) = x + 4. Use any rules for the following problems. 2. Differentiate the function f (x) = 7 −3 √ +x −2 x−ex +2 sin x x 3. Find the derivative of y = cos(x5 + 7x). 4. Find the rate of change of f (x) at x = 1 where f (x) = ( 1 3 x4 − )(x + ) x2 x3 4 5. Find all the values x where the graph of function y = horizontal tangent line. 6. Find an equation of the tangent line to the curve f (x) = ex 2x+1 ex 2x+1 has a at (0, 1). 7. Let the function be y = ex · cos x. (a) Find dy dx . (b) Find the second derivative of y, i.e., d2 y/dx2 . 8. Find the derivative of y = sin(tan(4x)). 9. Find the derivative of y = q x−2 x+2 .
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