For the following exercises, find f′(x)�′(�) for each function. 106.  f(x)=x7+10

Q: 5 ( 2xy +₁ e X = 1 Date 3 +2xy +y) dx + ( x²ÿ t ey - x ² y ² - 3 x) dy = solvo using Integrating…

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Q: Classify the equilibrium solutions as asymptotically stable or unstable. dy dt = y(y-4)(y-5), yo ≥ 0…

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Q: The top of a 22 foot long ladder is sliding downward at 1.6 feet per second along a vertical wall.…

A: Length of the ladder =22 footThe ladder is sliding down the wall at a constant rate = 1.6 feet per…

Q: The path of a diver is modeled by f(x) = − 4 x² + 24x + 9 + 13 where f(x) is the height (in feet)…

A: Given,

Q: Use the chain rule to find the derivative of f(x)=5(-527-82³) ¹4 Leave your answer in factored form.…

A: Consider the function

Q: Expand the quotient by partial fractions. 7x-27 x² - - 8x + 15 7x-27 x² - - 8x + 15 (Simplify your…

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Q: Use the method for solving equations of the form =G(ax + by) to solve the following differential…

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Q: 1) Let f be the function defined by f(x) = sin(2x) +ecosx . Let g be a differentiable function. The…

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Q: 4. Find the limits (a) lim x-1 (b) lim x-0 xª+¹(ln x + 1) − x 1-x ((² + 2)1/²) 1/². e

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Q: Calculate the derivative of the function. h'(x) = h(x) = (3.1x - 2)² - 1 (3.1x - 2)²

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Q: 5. a. b. C. d. The red squirrel population, p, in a neighbourhood park can be modelled by the…

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Q: Let g(x) = 6x³ + 7x7 +2r Determine the derivative of g. 70)- Determine the slope of g at = 1. g'(1)…

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Q: Given the equation below, find dy dx -54x7 +8x⁹0y+y¹0 90 = - 45 dy da Now, find the equation of the…

A: since you have posted multiple questions in this question which are not interlinked so i have solved…

Q: Given y = f(u) and u = g(x), find y=8u+1, u = dx (글)x 2 || 3 + dy ᆞ = f'(g(x))g'(x). dx

A: According to Bartleby guide line we only do first part of multiple questions.(A) y=8u+1,

Q: 1. Solve the equation between 0 and 2, 3 sin²(x) + sin(x) = 1 − 3 sin²(x)

A: We are given the trigonometric equation and need to solve it.

Q: Solve the given differential equation. All solutions should be found. dy x - 2y dx X

A: dydx=x7−2yx

Q: Find the first and second derivatives of f(x). Simplify your answer using positive fractional…

A: The given function is

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

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Q: Use partial fractions to find the inverse Laplace transform of the following function. s²-5s s4…

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Q: For the given cost function C(x) = 16900 +500x + x², First, find the average cost function. Use it…

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Q: Find a linearization at a suitably chosen integer near a at which the given function and its…

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Q: Let g(x, y) = { 2² 3x if x #y if x = y (i) Show that lim (x,y) (0,0) g(x, y) = 0. (ii) Determine all…

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Q: Classify the discontinuity in the following function. x²-12x+32 x-4 f (x) = The function has a jump…

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Q: part I of the Fundamental Theorem of Calculus to find the derivative of L = 3x + 6x y = cos (u7) du.

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Q: Problem 4: Let f(x)= 42-4 1²-1-6 a. Find the domain of the function. b. Find the y-intercepts, if…

A: The given function is,To find the domain, take the denominator=0So the domain is,

Q: Use the graphs of f(x) and g(x) to answer the questions below. Note - the graph of f(x) has a corner…

A: Given: Let To Find: To find the following:

Q: can you find C if x = 1/2 and y = (square root of 2)/2 thank you so so muchh!!

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Q: Let f(x) 2x + 1 - 4x 1 Then f'(x) Write the equation of the tangent line to f(x) at x = 1: = X

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Q: Find the critical numbers of the function. g(t) = t√13-t, t < 12

A: To find the critical numbers of the following function.

Q: Perform long division on the integrand, write the proper fraction as a sum of partial fractions, and…

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Q: Find the first and second derivatives of ƒ(z). Simplify your answer. 7 ƒ(x) = −3x7 P 2

A: Given,

Q: Find the area of the region enclosed by the curves y = || and y = 2

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Q: 6. A right circular cylinder with heighth and base radius r has a total surface area of 90 square…

A: (6) The surface area (A) of a right circular cylinder is given by the formulaA=2πr2+2πrh

Q: Use the disk method or the shell method to find the volume of the solid generated by revolving the…

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Q: Computek(k+1) k=1 Hint: Use the fact that Ek-1(ak-ak-1)= anao (this is called telescoping) and…

A: The given series .The aim is to compute the sum of the series.

Q: If the instantaneous rate of change of g(x) at (−1, −3) is 1/2, write the equation of the line…

A: The instantaneous rate of change of a function f(x) at a point (x,y) is the slope of the tangent…

Q: dy du du' dx' dy dx y = u53 and u = 5x4 - 2x² ind and

A: This is question of calculusHere differentiation given We have to do it.Further calculation is given…

Q: If f(x) = √2 + 5x, find f'(5), using the definition of derivative. f'(5) is the limit as x → 5…

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Q: if a list price is $10, what is the sale percentage of an item on sale for $8?

A: List price=$10Sale price=$8

Q: 22. Vectors word bank. Fill in the blank to describe the best choice. linear combination a parameter…

A: Given vector word bank,linear combination, a parameter, coincident, the scalar form, the normal, the…

Q: Find the velocity and position vectors of a particle that has the given acceleration and the given…

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Q: Let f be the function below. You may click on the graph to make it larger. W

A: Given graph of function

Q: Use implicit differentiation to find the derivative of y, where y is a function of x defined by the…

A: 3x2+9xy2=5x3

Q: Use implicit differentiation to find the derivative of y, where y is a function of x defined by the…

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Q: Consider the following function. Use a graphing utility to confirm your answers for parts (a)…

A: In this question, we will find critical point , Increasing or decreasing interval and Relative…

Q: y = (sin¯¯¹(x²)) tan-¹.

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Q: C₁ y = √x - 2 + 1 Show 4 pts, including the endpoint." (No decimals. Is no-calc. formative What are…

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Q: 3. a. C. Find the equation of the tangent to the curve at the given point. 3√x 5x2+1 y² = 2xy - 3,…

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Q: Find the Maclaurin series of Σ το sin(t) -dt.

A: To find the Maclaurin series of

Q: Find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the…

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