Differentiate. f(x) = 15x e f'(x) =

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Q: Find the arc length function for the curve y = 2x3/2 with starting point Po(16, 128) s(x) = ||

A: The given function is,The given point is,The lower limit of x is  and the upper limit is

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Q: 7. The arch of an underpass is a semi-ellipse10 meters wide and 4 meters high. Find the clearance at…

A: We solve the given problem by using the concept of the ellipse.

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Q: Find the derivative of the function. h'(x) = = h(x) = (arccos(x)) In(x)

A: To find the derivative of the following function.

Q: Simplify the rational expression. y³ - 27 -y² + 9y - 18

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Q: Use the formula above to determine how long it will take an initial investment of $6,750 to grow to…

A: given here initial investment is $6750 and 10.08% interest rate per year and it is compounded…

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Q: Find dy dx xy + y² = 5 dy-0

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Q: f(x,t)=x²+14x+y²-4y+3. Pls find maxima, minima, & saddle points. Thank you & I will give thumbs up.

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Q: Use the second derivative test to find the x-coordinates of all local minima given the following…

A: The given function is

Q: Find dy/dx by implicit differentiation. 9 cos(x) sin(y) = 1 dy dx

A: Given, 9cos(x)sin(y)=1.we know,

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Q: 4x(4-x2)1/2  Find the antiderivative

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Q: Find three positive numbers whose sum is 160 and whose product is a maximum.

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Q: 4. Find a formula for the nth derivative f(n)(x) of f(x) = ln(1+3x). Show some work computing the…

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Q: = OF MATHEMATICAL INDUCTION 2 (3") + 1 15 DIVISIBLE BY positive integer F E E

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Q: If f(x)= = 3x5 – 5x4 – 3x³ x4 " find f'(x).

A: The given function

Q: Determine the derivative dy da for each of the following equations.

A: (a) y=log8⁡(4)

Q: Suppose z = x² sin y, a = 48² t², y= 8st. A. Use the chain rule to find and all x, y, s and t in…

A: z=x2-t2 ,y=8st

Q: Change the order of integration. S J f(x, y) dy dx

A: given

Q: Suppose that the world's current oil reserves is R = 2180 billion barrels. If, on average, the total…

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Q: What is the characteristic polynomial of the matrix A = -24 0 8 -16 0 4 8 8 -20, For ease of entry,…

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Q: Match each scatterplot shown below with one of the four specified correlations. O O 00 %%0 O 08 Ⓡ 0%…

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Q: Pharmaceutical firms invest significant money in testing any new medication. After the drug is…

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Q: Which of the points P = (-1,4,-7) and Q = (6,-1,5) is closest to the z-axis? OQ (6,-1,5) OQ (6,-1,0)…

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Q: The population of Vero Beach can be modeled by the function P = 17234e0.01921t where t is the number…

A: where t is the number of years since 2020

Q: If f(x) = 4√√x(x³ - 8√√x+6), Find f'(2). find f'(x).

A: If .To find .

Q: Problem 3 Find the areas of the following regions contained in the (x, y)-plane. (1) R = {(x,y) :…

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Q: Use the chain rule to find and where First the pieces: 8/8 8/3 3/5 |||||| || ||||70 And putting it…

A: Consider

Q: A ball is thrown downward from the top of a 20 m tall building with an initial velocity of 15 m/s.…

A: Given that height of building is 20m. And initial velocity is 15m/s. We find the equation of height…

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Q: Let f'(x) = 12x5 lnx + 2x³ f'(e²) = f(x) = 2x6 ln x

A: given here f(x) and asked to find f'( e2 ).

Q: Find the time it takes for $6,400 to double when invested at an annual interest rate of 14%,…

A: Formula for compounding continuously, .Where A is final amount, P is initial amount, r is rate, t is…

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Q: Given the function f(x) = 7x+3 - 9e Determine the equation of the tangent line at the point (0, -6).

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Q: Use the Chain Rule to find dz dt 1 where z = 3x siny, x = t², and y = 2t4.

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Q: Find the length and direction of u x v. u=4i+2j+8k, v=-i-2j-2k

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Q: 2. For the function f(x) defined by the graph below, with each mark representing one unit, evaluate…

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Q: Due Math 31 Chapter 9 Review Assignment 1. Verify y(x)=c, sin x + c₂ cos x-(cos x)In(secx + tan x)…

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Q: Solve the differential equation. du dt = (5t^4)/(ut^2+u^4t^2)

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Q: Find the an equation of the hyperbola satisfying the given conditions. Foci at (-13,0) and (13,0);…

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Q: In(19/t+1) 4/t Minimum Level of Stabilization: 2.73125 Maximum Level of Stabilization: 3.740625…

A: Minimum level of stabilization: 2.73125Maximum level of stabilization: 3.740625

Q: 5. §11.5. Q31. Use a chain rule to find the value of dw dxs=1/4 if wr² - rtan 0, r = √s, 0 = πs.

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Q: Given: x=t², y=t-8, -4≤t≤4 a) Sketch the curve by using the parametric equations to plot points.…

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Q: Let A be a 2 x 3 matrix and T: R³ → R² be the linear mapping T (7) = A 7. 2 (6) - A) ¹ (1) - ()-[²]…

A: Consider the linear transformation

Q: alculate the derivative of the following function. y = (p+e)5 sin p³ 3 ***

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Q: Given function f (x) = x3 − 12x + 2, (a) find the intervals of increasing or decreasing (b) find…

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