(3 pts each) Find the derivatives of the following: DO NOT SIMPLUFY. Circle your answer a. (x) (3x* +7x)6 c. y In (3x-6x + 2) (3 pts each) Find the derivatives of the following: DO NOT SIMPL...
Question 2: Find for the following functions: (1) y=-42x2-3x -! 7x? -5x + 9 (3) y= x+5 (5) Y= 7+3 (y = (3x* + 3x + 2)(x+1) (7) y =(5x + 7x) Page 1 of 2 Question 3: (0) Find the slope of the graph of y=f(x) = 3x - 6x +1 at the point (2,1) (ii) Find the equation of the tangent line to the curve y = f(x) = x*-10x2 + 9 at x=-1 (iii) Find the equation...
Find all the second-order partial derivatives of the following function. w=3x sin (6x²y)
6 of 15 (complete) Find all the second-order partial derivatives of the function f(x,y) - 7x + y + xy (Simplify your answer) dyche (Simply your answer) 21 dy (Simplify your answer (Simply your answer Enter your answer in each of the answer boxes
. Find the first derivatives (dy/dx) for each of the following functions. Do not need to simplify. (3 points each) A. y = (2x^5 + 3x^3)^2 B. y = (8x^3-56x^2+3x)/(x+12) C. y= (6x2 + 3x) (x – 4x3)
2. (2 pts) Determine the type of the critical point (0,0) for the system x' =-7x+ 5y, y' =-6x 4y. Sketch a phase portrait based on the eigenvectors, and the direction that the sign of the eigenvalue indicates. 2. (2 pts) Determine the type of the critical point (0,0) for the system x' =-7x+ 5y, y' =-6x 4y. Sketch a phase portrait based on the eigenvectors, and the direction that the sign of the eigenvalue indicates.
Find C(x) if C'(x)=5x2 - 7x+4 and C(6) = 260. + 4x + 2 O A. C(x) = 5x2-3x+ O B. C(x) = 5x2-3x +4x-260 O C. C(x) = 3x + 4x-2 5 7 OD. C(x)= 3x - 3 + 4x + 260 ces ary Click to select your answer
Find the quotient using long division. 21. 3x+11x+6 x+3 3x+11x+6 (Simplify your answer.) x+3 22. First factor out the greatest common factor from each term. Then factor the remaining polynomial. 3x +3x-60 3x2 +3x-60 Factor the trinomial completely. 23. 7x-20x-3 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA T-20x-3 (Factor completely.) O B. The polynomial is prime. Use the difference of two squares formula to factor the polynomial. 24. 9-64b2...
EXAMPLE 2 Find sin$(7x) cos”7x) dx. SOLUTION We could convert cos?(7x) to 1 - sin?(7x), but we would be left with an expression in terms of sin(7x) with no extra cos(7x) factor. Instead, we separate a single sine factor and rewrite the remaining sin" (7x) factor in terms of cos(7x): sin'(7x) cos”(7x) = (sinº(7x))2 cos(7x) sin(7x) = (1 - Cos?(7x))2 cos?(7x) sin(7x). in (7x) cos?(7x) and ich is which? Substituting u = cos(7x), we have du = -sin (3x) X...
3x+2 f(x) =( :) (x-> +1) Your problem: using the rules of differentiation, find the derivatives of the collowing: f)-(3442) fool(3x+2) (-5x + x + 1) - 2 1 =(-15x 10x" + (-2x = 2) =>15x410x5 - 2x = = 3x -3x- 27 (X)(3+0)-(3x+2)(1) x² g'=(x) =F12x15x4_2 = -5x6 xb * please check my work, if wrong, please write out correct solation! Chain Rule: When functions are composed, to take the derivative involves both the outside function and the inside...
find the maximum value of z=6x-3x^2+2y (subject to y-x^2=2 if condition changes to y-x^2=3, how much will z increase?