5. Differentiate the following functions by filling in the chart. Original Function Rewrite Differentiate Simplify a....
#35,37 In Exercises 21 through 38, differentiate the given function and simplify your answer 21. f(x) (2x 3)14 22. fx) 23. f(x) = (2x + 1)4 24. f(x) = V 5x6-12 25. fx)-(a 4r3 78 26. ft) (3r 729)5 27, f(t) = V5 3x 28. f(x)=- (6x2 +5x+ 1)2 5rt_ V4x2 30. 4x +1 31. f(x)=: (1-x2)4 2 3(5x4 1)2 32. f(x) = (1-x2)4 (135) f(x) = (x + 2)3(2x-1)5 36. f(x) 2(3x 1)(5x 3)2 (1 -x 1 - 5x2...
Prob.II. Differentiate the following functions, and simplify. 1. f(x) 2x-3 x+4 2. f(x) = x²(x - 2)* 3. f(x) = In (x V1 - x2) 4. f(x) = x2e-* 5. Find dy/dx = y' for the equation x2 + y2 = 25 and find y" (check H.W)
Differentiate the function ??(??) = ??4 ln(5??) + ln ( 3??+2 2??−3 ) 3x+2 Differentiate the function f(x) = x4 ln(5x) + In 2x-3 For full credit show each step. You do not need to simplify the answer. (10 points)
3. (6 points each) Differentiate the following functions. Do not simplify your answer. a. f(x) = 2*+1 In (x+1) b. p(x) = [arctan (x)]3 c. Q(x) = ex-sec(x)
For the following functions and using Boolean identities a) Simplify the given functions b) Construct the truth table for both of them showing the output of the original function and the simplified one and compare the two outputs? c) Draw the logic circuits for both the original function and the simplified one? 1. FIX, Y, Z) = X'+Y' + XY'Z 2. F(X, Y, Z) = (X+Y)(X' +Y+Z)
Name: Lab 3: Differentiation An example to differentiate an expression: To assign the expression 2x-5x+x to the variable fenter: f:-2*x^3-5 *x^2 +x; To enter f(x) -2x3-5x+x as a function enter: f:=x->2*x^3-5*x^2+x To differentiate some function fenter: D (f); To differentiate some diff (f,x) ; expression f with respect to x enter: Now follow the steps in the Example above to differentiate the expression t-1 Keep in mind that you cannot use the variable f for the expression (we already used...
2. (4pts each) Find the derivative of the following functions: You do not need to simplify the answer. CIRCLE FINAL ANSWER. a. f(x) = 2x2e-1 + 7e2x-1 + 3e2e cos (36) b. g(t) = 1+sin(3) c. h(x) = ln(x2). arctan(kx) (k E R) d. f(x) = sin(x) sin(x)
13. Rewrite the following expression as a single logarithm and simplify where possible: [5 Points) 4. log6x + log6(x - 1) -10964 14. Use the Remainder Theorem to determine if (x - 4) is a factor of f(x) = x3 – 3x2 - 10x + 25. If it is a factor, use polynomial or synthetic division to help you rewrite f(x) in fully factored form. [5 Points]
2. Find the intervals on which the following function is continuous. tan r B( ) = V4-12 3. Find the derivatives of the following functions (a) f(z)= /5x +1 (b) gla) = (2r -3)(a2 +2) (c) y = In (x + Vx2 - 1) 4. Find the intervals on which the following function is decreasing. f(z) = 36x +3r2 - 2r 5. Evaluate the following integrals. r dr (a) sec2 tan (b) dar 3 (c) da 5x+1 1. Sketch the...
please answer both questions Use logarithmic differentiation to differentiate the following function. f(x) = e * (5x - 6) f'(x)= Which of the following is the same as 2 In (8x)? (a) In 16+ Inx (c) In (16x) (b) 16 In x (d) In (64x2) List all expressions that are equivalent. (Type a, b, c, or d. Use a comma to separate answers as needed.)