Differentiation Questions and Answers

Let g(v) = 4e^v / v-9 Determine g'(v) g'(v) =

Let f(y) = (-2+3/y) /y+1 Determine the derivative of f. f'(y) = Determine the interval(s) on which f is differentiable. Report the solution using interval notation. f is differentiable on

Let g(w)= [(w+1)/(w-5)]*(8w - 7) Determine g' (w) g' (w)=

Let f(v) = 9-v / 1-v Determine the derivative of f. f'(v) = Determine the interval(s) on which f is differentiable. Report the solution using interval notation. f is differentiable on

Let g(x) = x³ {5+ 2/(x-5)} Determine the derivative of g. g'(x) = Determine the slope of g at x = -2. g'( - 2) =

If f(x) and g(x) are continuous functions and c(x) = f(g(x)) use the table below to evaluate c'(-2). x f(x) g(x) f'(x) g'(x) -2 -5 2 1 -3 -1 1 1 2 -1 0 4 -4 0 3 1 -1 -3 -5 4 2 -4 -2 -4 2 Enter your answer in the space below.

Let h(u) = (6u + 8) (-3u + 8) (- 8u - 8) Determine dh/du

Let h(w) = - 5w³ (w³-7) Determine the derivative of h. h' (w) = _____________. Determine the interval(s) on which h is differentiable. Report the solution using interval notation. h is differentiable on

Let f(z)=√(8-4z³) Determine the derivative of f. f'(z) = Determine the interval(s) on which f is differentiable. Report the solution using interval notation. f is differentiable on

Let f(x) = x²h(x) and h have the following properties. • h(5) = 1 • h'(5) = 3 Determine f'(5). f'(5) =

Let g(v) = -(-6v^2)/ (v-3) Determine the value(s) of v, if any, for which g has a horizontal tangent line. A) g has a horizontal tangent line at v = B) g has no horizontal tangent lines.

Let f(x)= (-2x²-3x - 8)/9 Determine df/dx

Use Matrices to find the equation of the quadratic polynomial that goes through the points (-2, 79) (0, 7) and (1,1).

Let L: R² → R² be the linear operator given by the rule L(x, y) = (5x+3y, -4x - 2y). Find an ordered basis B for R² such that [L]ᵇ =[2 0] [0 1] a)B={(-1,3), (4, -1)} b)B = {(-1, 1), (-3,4)} c)B= {(4,3), (1, -1)} d)B= {(2,0), (0, 1)} e)B= {(4,-1), (1, -3)}

Given f(x)=x/(x+3) and g(x)=2/x , find (fog)(x). What is the domain of the composition?

Find the rate of change of f(x)=x²+5x-12 on the interval [0, a].

A truck with 32-in.-diameter wheels is traveling at 50 mi/h. Find the angular speed of the wheels in rad/min, "hint convert miles to inches & hours to minutes: _______ rad/min How many revolutions per minute do the wheels make? ______ rpm

Maya earns 41 dollars per week working part-time at a book store. She makes one dollar more for each book that she sells. The amount, A (in dollars), that Maya earns in a week if she sells b books is given by the following function. A (b) = 41+b. How much does Maya earn in a week if she sells 28 books? __________ dollars

1. Calculate y'. y =√x.cos√x 2.. If f(x)=4cosx+sin²x, find f'(x) and ƒ"(x).

Determine how many x-intercepts the function y = 3 cos x + 5 has from 0° to 360°. A) 0 B) 2 C) 4 D) 6

Solve for all values of x. 343^(2x+16) = (1/7)^(-2x²+4x)

Find all the complex square roots of w =144 (cos 30° + i sin 30°). Write the roots in polar form with θ in degrees. z₀ = __(cos__° + i sin__°) (Type answers in degrees. Round to the nearest integer.) z₁ = __(cos__° + i sin__°) (Type answers in degrees. Round to the nearest integer.)

The gas law for an ideal gas at absolute temperature T (in kelvins), pressure P (in atmospheres), and volume V (in liters) is PV = nRT, where n is the number of moles of the gas and R = 0.0821 is the gas constant. Suppose that, at a certain instant, P = 7 atm and is increasing at a rate of 0.10 atm/min and V = 10L and is decreasing at a rate of 0.15 L/min. Find the rate of change of T with respect to time at that instant if n = 10 moles.

Solve using Cramer's Rule. x +y +z = 11 X-y +z = 3 2x + z = 12 What is the solution of the system?

Find the first derivative of the function f(θ) = sin((e^2θ)/(1+e^2θ)). Then evaluate the first derivative when θ=π/2

9. Find the derivative of the function f(x)=sin¯¹(x³ + 1) 10. Suppose that F(x)=f(g(x)) and g(14)=2, g'(14)=5, f'(14)=15, and f'(2)=12. Find F'(14).

Solve using Cramer's rule. 12x + 27y= -6 24x – 9y = 9 The solution is (Simplify your answer. Type an ordered pair, using integers or fractions.)

A ray of light passes from air (n=1.00] into water (n=1.33) at an angle of incidence of 50°. What is the angle of refraction?

You are on a boat in the middle of the Pacific Ocean at the equator traveling in a hydrofoil going at a constant speed of 300 m/s. The water is perfectly still. What is your acceleration: a) If you're heading due North? b)If you're heading due East? c) If you're heading straight up (something probably went wrong at this point). You may assume the following: The earth has a radius of 6371 km. The earth makes one full revolution every 24 hours. The gravitational constant at sea level is 9.81 m/s² East and North are relative to the Earth's axial north, not magnetic north.

Find the exact value. sin(17π/12) a) Write the given angle 17π/12 as a sum of two special angles: Enter the combination with the smallest angle first. Enter the smaller angle on each possible combination. 17π/12 = _____ OR 17π/12 = _____ OR 17π/12 =_______ b) Use one of the combination to Sum/Difference Formula to evaluate exactly. sin(17π/12) = ______

• Use logarithmic differentiation to find the derivative of the function. y = (3x+1)³(x⁴-6)³ • Use logarithmic differentiation to find the derivative of the function y = x⁶^x

Let h(t) =t³ (-8+8/t-5) Determine the derivative of h. h' (t) =____ Determine the slope of h at t = - 9. h'(- 9) =___

The edge of a cube was found to be 30 cm with a possible error in measurement of 0.1 cm. a) Use differentials to estimate the maximum error in computing the volume of the cube. b) What is the relative error? What is the percent of error?

Let f(x) ={(9-7/x)/(x+5)} Determine the derivative of f. f'(x)= _______ Determine the slope of f at x = -9. f'(- 9) = ______

Let h(v)= 1/v⁷ Determine the derivative of h. h'(v) = Determine the interval(s) on which h is differentiable. Report the solution using interval notation. h is differentiable on _______

Let f(w) = (-w-8)(6w+1) Determine the derivative of f. f'(w) = _______ Determine the interval(s) on which f is differentiable. Report the solution using interval notation f is differentiable on _______

Let y = f(x) and x = g(t). If g(1)=2, f(2)=3, g'(1)=4 and f'(2) = 5, find the derivative of f∘g at 1.

Let g(x) = 2 cos(x) - 8 tan(x) Determine d/dx [g(x)] d/dx [g(x)]=

Let h(t) = sin(t) Determine the one hundred seventieth derivative of h. h (¹⁷⁰) (t) =?

Let f(v) = 6ᵛ Determine the two hundred forty-eighth derivative of f. f(²⁴ ⁸) (v)=?

Let h (v) = -6v + log₁₃ v Determine the seventh derivative of h. h (7) (v) =

Let f(z) = 7eᶻ sin(z) Determine the second derivative of f. f''(z) =?

Let X and Y be two independent random variables with distribution functions Fx and Fy. (a) Show that φxy(t) = ∫ φx(tx)d Fx(x). (b) Show that ¹∫₀ cos(tx0dx is a characteristic function. (c) Show that φx + y(t) = φx(t) φy(t).

Given the function f(x)=4x+5, find and simplify the following values: f(a) = __________________ f(a+h) = ___________________ (f(a+h)-f(a))/h = ___________________

If f(x) = In(2x)/x, what is the value of f'(1/2√e) in simplest form?

Use the tangent identity to find tan x. sin x = (2√10)/7 cos x = 3/7 tan x = [?]√___

In Exercises 33-42, find the slope-intercept form of the equation of the line that passes through the points. Use a graphing utility to graph the line. 33. (5, 1), (-5,5) 38. (1, 1), (6, −3)

A radioactive substance decays so that after t years, the amount remaining, expressed as a percent of the original amount, is A(t) = 100(1.3)¯t. a) What is the half-life for this substance? Round to 2 decimal places. b) Determine the rate of decay after 10 years. Round to 2 decimal places.

Let f(y) = 3 csc(y)cot(y) Determine df/dy df/ dy = ______

Let g(w) = 2w + log₅w Determine the seventh derivative of g. g (7) (w)=___