The given problems need the first derivative. Find the first derivative. y = 3x + 6 y = x2 –1

Q: 15 4 -4-3 -2 4 2- -3 3.

A: Accordimg to given graph a. As x→-2-  fx→∞b. As x→-2+  fx→-∞

Q: Find fy (x,y,z), fy(x,y,z), f_(x,y,z), and fyx(x,y,z) for the following. f(x,y,z) = 3x* + 3xy - 5z

A: We need to find derivative of given function.

Q: (2a+1) (x+2) (x–1)

A:

Q: dy When solving the Bernoulli DE: x - = , which of the choices is utilized for (1+x²)y substitution ...

A:

Q: In a time of t seconds, a particle moves a distance of s meters from its starting point, where s = 6...

A:

Q: Find the area enclosed by the x-axis and the curve y = -x² + 9. 32 A.) s.u. B.) 18 s.u. C.) 36 s.u. ...

A: Follow the procedure given below.

Q: x5 dx (x6-8)2 2.

A: given that,  evaluate the following integral ∫x5(x6-8)2dx integration formula   ∫xndx=xn+1n+1+C

Q: Show that f(x,y) = 1-x* - y* has a relative maximum, even though D in the theorem is 0. The critical...

A: Given : f(x, y) = 1 - x⁴ - y⁴

Q: g(x) = 2f(1 – x) +3. find a correct order of the following ransformation: reflection in the y axis h...

A: Given query is to find the transformation applied.

Q: 4. -[lp A~ q) A r] = ¬p V q V ¬r 5. -[p → (¬q)] = p A q 6. (p → r) A (q → r) = (p V q) → r

A:

Q: Question 11 Зсos3x-1 To evaluate f scos - dx, the integrand can be transformed to 1-sin?x A.) [(3cos...

A: We put 1-sin2x=cos2x and then solve it. Follow 2nd step.

Q: What is an antiderivative of ... x²+1 x + arctan x – 5 2x + 3 x + arccot x x + 2arctan x + 1 А) в B)...

A:

Q: Using the fact that the centroid of a triangle lies at the intersection of the triangle's medians, w...

A: We can find the centroid as below using the required formula.

Q: 18( cos54 + isin54°) 3(cos102" + isin102" )

A:

Q: The rate of change in the profit (P) with respect to the number of units sold (x) is 0.0006x2 + 10. ...

A: Given, P-profit x-number of units sold dP/dx= 0.0006x²+10  

Q: What should be the rewrite of the integrand of dx so that the resulting integral is integrable?. 4+2...

A:

Q: What value(s) of o are an appropriate choice when proving the following limit? lim (2 + 9x + 25) = 5...

A:

Q: 17. A boat is being pulled toward a dock as shown in the figure. If the rope is being pulled in at 3...

A: Follow the procedure given below. 

Q: In Problems 35-40, find f' (x) and the equation of the line tangent to the graph of f at the indicat...

A: Given query is to find the equation of tangent line.

Q: Solve each equation for x. (For each answer, enter an exact number. (a) e5x + 9 - 4 = 0 X = (b) In(4...

A:

Q: Find the slope of the curve at the indicated point. find the equations of the tangent and normal lin...

A: Follow the procedure given below.

Q: 3. Find the indicated values. a) f(x) = x³, g(x) = 6. (f°g)(x)? b) f(x) = -2x + 1, g(x) = x², h(x) x...

A:

Q: uity?

A: We will find the functional value at x=2.

Q: Suppose the labor cost (in dollars) for manufacturing a camera can be approximated by L(x.y) =x +y -...

A: Given: Suppose the labor cost in dollars for manufacturing a camera can be approximated by Lx, y=32x...

Q: Given a function f (x) whose graph is shown below. (6,5), (1,4) (-4,2), 2 (6,2) -6 -4 -2 2 4 -2마 9(1...

A:

Q: Question 15 Determine the equation of the curve whose tangent line at any point (x.y) is e* – sin x ...

A:

Q: If dx dy and y = 27 14 when x = 1, find y(2). %3D 3x-2

A: ∫x3x-2dx

Q: (2x+5)² 19. What should be the rewrite of the integrand of S -dx so that the resulting integral is x...

A: Given query is to rewrite the integrand in integrable manner.

Q: (1+2 In æ)4 -dx

A: Indefinite Integration using substitution

Q: Evaluate f x+3 x3+27 dx.

A: Our Aim is to evaluate the integral given below:-∫x3+27x+3dx -(i)

Q: f(x,y) = 100x062y0 38. Find the marginal productivity of labor and capital.

A:

Q: Use the function f(r) given below to answer the questions that follow. f(r) = – 2(r+1)(r – 3) (r – 1...

A: The given function f(r)=-2r+1r-33(r-1)

Q: f(x) C B. A D (a) At which of the labeled points isf' (x) positive? Negative? Zero? f'(x) is v at A....

A: f'(x) at any point means slope of the tangent line drawn at that point. If  tangent line makes an an...

Q: In Problems 39- 42, find the equation(s) of the tangent line(s) to the graphs of the indicated equat...

A:

Q: 21. The radius of a spherical balloon is increasing at the rate of 3 centimeters per minute. How fas...

A:

Q: 25. A 10-foot ladder is placed against a vertical wall. Suppose that the bottom of the ladder slides...

A: Given :-  dx/dt= 3feet/sec  Ladder height= 10feet  Find rate at which ladder is sliding down from th...

Q: Determine the equation of the curve whose tangent line at any point (x,y) is e* – sin x and passes t...

A:

Q: An object is shot upwards from ground level with an initial velocity of 3 meters per second; it is s...

A: Let's find. 

Q: An object is shot upwards from ground level with an initial velocity of 3 meters per second; it is s...

A: Let's find. 

Q: Write an equation for a cost function where the fixed costs are $2300 and the variable costs are $20...

A: Given data: Fixed cost= F= $2300 Variable cost=V= $20

Q: 15. A particle moves along a straight line and has acceleration given by s"(t) = 5t + 3. Its initial...

A:

Q: LINEAR DIFFERENTIAL EQUATION WITH CONSTANT COEFFICIENTS (STEP BY STEP SOLUTION) (D4 - 1)y = e*

A: Please see the below picture for detailed solution. 

Q: Solve the given differential equations FODE.  Solve each and show complete solution.    (3x – y – ...

A:

Q: Evaluate the integral. | cos (x)dx

A: The given integral is: I=∫cos-1x dx

Q: 10

A: Evaluate the integral ∫4x4+310dx

Q: 3cos3x-1 uate f dx, the integrand can be tran 1-sin2x Bcos3x + csc²x)dx

A: We have to choose the correct answer from the given options according to the given information

Q: Breble Find the volume of the solid whose base is the region inside the unit circle x2 + y? = 1, and...

A: We need to find volume.

Q: Find the x-coordinate of the first point in the region æ > 0 where y = 2x intersects y = tan r. Give...

A: Given y=2x Y=tanx

Q: A company’s total sales (in millions of dollars) t months from now are given by S(t) = 3 + √t  a. Fi...

A: Given s(t) = 3+tinstantaneous rate of change is given by     R = ds(t)dt

Q: What is the position function?

A: