If f(x) = x5(4x + 5)6, compute the first and second derivatives of f(x). f'(x) = f"(x) =

Q: ff.

A: The given equation is; x=(wt+B).

Q: What happens if you take B = A in the trigonometric identitycos(A - B) = cos Acos B + sin Asin B?…

A: The given identity: cos(A - B) = cos Acos B + sin Asin B To check what happens if B = A .

Q: PLOT THE GRAPH FOR THE GIVEN CURVES AND CONDITIONS BELOW Need to find out the differential equation…

A:

Q: 1. Consider the hyperbola with foci (-6, 1) and (-6, -9), and a vertex at (-6, -1). a. Give the…

A: Given 1. foci -6, 1 and -6, -9 2. Vertex at -6, -1

Q: Find the limit. (If an answer does not exist, enter DNE.) lim arctan(eX) x → ∞0

A: We have, limx→∞ arctanex

Q: 9. y = ln *³(x-¹)(use properties of logarithms) (x+1)4

A:

Q: Newton's law of cooling relates the rate at which a body cools to the difference in temperature…

A:

Q: In Exercises 9-16, verify each limit using the limit definition. For ex- ample, in Exercise 9, show…

A: To verify each limit using the limit definition.9 limx→4 3x=12 10 limx→5 3=3

Q: Let y = √√x. y'' = y''' =

A:

Q: Which function shows f(x) decreasing as a approaches negative and positive infinity? Select all that…

A:

Q: 2. Identify an inner function u = g(z) and an outer function y = f(u) of y=e=¹+2 3. Express Q(z) =…

A: Solution

Q: Compute the first-order partial derivatives of the function. 16x √x² + y² (Use symbolic notation and…

A: Given, z=16xx2+y2

Q: Find dy/dx using partial derivatives  cos(x-y) = xe^y

A:

Q: For what value of p does the sum of roots of the equation 6x² - 3px + 5 = 0 equal the product of…

A:

Q: Find the parametric equations of the intersection of the planes x + (y − 9) + z = 0 and −x + (y + 9)…

A:

Q: dx xinx 6. S

A: Given integral ∫dxx ln x Formula ∫1xdx= ln x + C

Q: please indicate email and solution. thank you

A: To find whether S is linearly independent or not.

Q: a. Graph the function ƒ(x) = sqrt(1 - x2), 0<= x <= 1. What symmetry does the graph have?b.…

A: The given function is: f(x)=1-x2,0≤x≤1. It is required to find the symmetry of graph.

Q: Compute the first-order partial derivatives of the function. z = tan (3uv4) (Use symbolic notation…

A: We have to find the partial derivatives.

Q: On equation (iv), why is d/dz of 3z^3 is equal to 3z^2, shouldn't it be 9z^2?

A: Yes, you are right. There is mistake in equation (iv). Correct solution is shown below.

Q: The fuel economy (in miles per gallon) of a certain car is E(x) = −0.01x2 + 0.58x +10.4, where x is…

A:

Q: 4. (x + y)dy - (2x - y + 3) dx = 0

A: The differential equation Mdx+Ndy=0 is said to be exact if ∂M∂y=∂N∂x. The solution of the…

Q: Which of the following functions is homogeneous of whose degree of homogeneity is 4. A. f(x, y) =…

A:

Q: 4x² . Let y=f(x) = 4x+1

A: Topic:- application of derivatives

Q: C. S 9dv 81-24

A: Part c,Given,            ∫981-v4dv

Q: Find d2y/dx2 if x = 3 - 2z and y = z2 - 3z3

A:

Q: c) fsin-¹(x) dx -1

A:

Q: Use any method to set up an equation to find the volume of the solid generated by revolving the…

A: We need to set up integral.

Q: 2y Suppose f(x, y) = sin X in the direction of (1, 2). Then, 2y 2y i (a) ▼ f(x, y) = cos(2)21 +21) X…

A:

Q: 1) Consider the function f (x) = 2x³ - 3x² Fill in each blank with the correct numerical answer. a)…

A:

Q: Use any method to find the volume of the solid generated by revolving the region bounded by the…

A:

Q: . For what values of r does the function y = er* satisfy the differential equation y" - 4y' + y = 0?

A: Please see the below picture for detailed solution.

Q: DIRECTIONS Indicate the degree and determine the solution of the following equations. 3. (x² + 2xy…

A:

Q: The demand function for a certain brand of compact discs is given by where p is the wholesale unit…

A:

Q: 6 5 4 3 2 1 y = f(x) 012 lim h→0 = lim f(f(x) + 1) = x → 1- 3 I f(0 +h)-f(0) h I 4 5 I I Enter each…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find the required value by setting up the general equation and then evaluating. Find s when t-4.0 if…

A: Given:s is inversely proportional to the square of t.Ands=3 when t=8

Q: Find an equation of the line that satisfies the given conditions. Through (−4, −5); slope − 7/2

A: Given, line passing through (−4, −5) and having slope − 7/2

Q: Match each function f with a function g so that (fog)(x) = x². (x² + 2)² (²-2)² x² - 2x + 1 :: 2 ln…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: The point 2 is in the range of the function given by f(x, y) = True False 2x² x² + y²

A: We can check whether the statement is true or false .

Q: K Let f(x) - f''(x) = 3 + 3 x6

A:

Q: f(x)=ln(x^5) f′(x)= f′(e^3)=

A: Given query is to find indicated derivative.

Q: If f(x) = (4x + 1)5, compute the second derivative f"(0) : =

A:

Q: Find the partial fraction decomposition of the integrand. 3 'x(x²+5)* dx = O dx

A:

Q: Check that the point (−2, 2, 4) lies on the surface cos(x + y) = exz+8 (a) View this surface as a…

A: To find the normal vector to the surface.

Q: (1 + 1) ds + 2s = 3(1 + 1) + 12. (t 1 (t + 1)²¹ t> -1

A:

Q: Let f(x) = x-4. You apply (in the order given) all of the following transformations to f(x) to get…

A: Given query is to apply the transformation and find the new function.

Q: For the given function, find all as f(x) = 2 Ex 7x² + 12x - 4 +1

A:

Q: 5. Bernoulli's Equations b. 2x³y' = y(y² + 3x²)

A: equation

Q: Solve the ff. Linear Equation: c. 2 2x³y = y(y² + 3x²)

A: We have to solve this given Bernouli's Differential Equation.

Q: Evaluate: S 5x²-3x+2 dx x³ - 2x²

A: