Practice Altogether Derivatives of Transcendental Functions Directions: Evaluate the following items. Write your solutions on a separate sheet of paper. (10 items x 5 points) 1. ~ sin?(x2 + 2x + 1) 2. - [4 tan(3x3) - 5 cscx] 3. sin 4 . - (4 sin 3x - x) 5. (x cos 5x2) 6. dx x2 7. ~ tan Vx2 + 1 2 8. dx (cos 2x) 9. Vcsc 5x cot 5x 10. ~ (4x2 sec x tan 3x) Rubric: Criteria Points Complete and correct solution 5 Last two major steps of the solution are incorrect Half of the solution is correct 3 First two major steps of the solution are correct N First major step of solution is correctRules in Action Derivatives of Algebraic Functions Directions: Prove the following statements. (4 items x 5 points) 1. If f(x) = (x2 -1)3 then f' (x) =6x5 - 12x3 + 6x. 13x7 + 20x4 2. If f (x) = x5\\x3+2 then 2Vx3 + 2 X 1 - x2 3. If f(x) = then f'(x) = Vx2 + 1 2x(x2+ 1)3 4. If f(x) = (V4x2 +8- 12)- then f' (x) = - (8x + 4x3) V4x2 +8- 24x3 - 32x V4x2 +8 Rubric: Criteria Points Complete and correct proof 5 Last two major steps of proof are incorrect. Half of the proof is correct. - NWA First two major steps of the proof are correct. First major step of proof is correct.How do you prove a function is a derivative? Proof of Sum/Difference of Two Functions : (f(x)+g(x))'=f'(x)+g'(x) This is easy enough to prove using the definition of the derivative. We'll start with the sum of two functions. First plug the sum into the definition of the derivative and rewrite the numerator a little. Jan 22, 2019 https://tutorial.math.lamar.edu > calci Calculus I - Proof of Various Derivative Properties - Pauls Online Math NotesThe three basic derivatives (D) are: (1) for algebraic functions, D(x) = nx - 1, in which n is any real number; (2) for trigonometric functions, D(sin x) = cos x and D(cos x) = -sin x; and (3) for exponential functions, D(ex) = ex. https://www.britannica.com > science ... differentiation | Definition, Formulas, Examples, & Facts - Encyclopedia BritannicaDerivatives of transcendental functions The new material here is just a list of formulas for taking derivatives of exponential, logarithm, trigonometric, and inverse trigonometric functions. Then any function made by composing these with polynomials or with each other can be differentiated by using the chain rule, product rule, etc. (These new formulas are not easy to derive, but we don't have to worry about that). The first two are the essentials for exponential and logarithms: d = 6 dx d 1 In x = dx The next three are essential for trig functions: d sin x = cos x dx d cos x = - sin x d tan x = sec x dx The next three are essential for inverse trig functions 12 1 arcsin * = dx VI 7-2 d 1 dac arctan * = 1 + x2 d arcsec x dx ac Vac2 - The previous formulas are the indispensable ones in practice, and are the only ones that I personally remember (if I'm lucky). Other formulas one might like to have seen are (with a > 0 in the first two): d a" = In a . al dx d loga C = dac In a . x d sec x = tan x sec x da d csc x = - cot x csc x dx dac cot x = - cscac 2 -1 dac arccos C = V1 - d -1 arccot x dx 1 + x2 d arccsco = dx ac Vac2