Find the derivative of the function. F(x) = (x4 + 9x² - 3)5 F'(x) = X

Q: Continuing with the same graph of f(x), which value is the greatest: f(5), f'(5), or f(6) -f(5) ?…

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Q: Need Help? m/min. Read It Watch It Master It

A: Topic:- application of derivatives

Q: In Exercises 13-18, use an inverse matrix to solve the system o linear equations. 13. x + y + 2z = 3…

A: The objective of the question is determine the solution of the given system of equations help of…

Q: Show that for integers a, n satisfying 0 < a <n, ged(a, n) = gcd(n, n-a)

A: Solution is given below:

Q: Use the Laplace Transform to solve the giver initial value problem. y" + 2y + 5y = 0; y(0) = 2,…

A: Given Differential Equation:- y''+2y'+5y=0;y0=2,y'0=-4

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Q: DDD

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Q: dy Use implicit differentiation to evaluate at the point (-2, 1). dx (Submit an exact answer.)…

A: Topic = Derivative

Q: x 1 3. Bauh. Bd. J... A Xdy. (X² 3y).d.x.=... Jo 2 ....................

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Q: Find the general solution of the given differential equation 2y" + 3y + y = t² + 3cost

A: Given:2y''+3y'+y=t2+3costhere y'=dydt and y''=d2ydt2

Q: 2+2+2+1 de

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Q: The Chain Rule Exercise 8 y = (3.x²+1)³: (a) Decompose the function in the form y = f(u) and u =…

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Q: 18,000 invested compounded for 6 years at 4% interest. How do I figure out the annual and semi…

A: 18,000 invested compounded for 6 years at 4% interest. To determine the annual and semi annual…

Q: Chain Rule (One independent variable) Let z(x, y) = 2e* sin(y) where x = t' & y = 5mt. Calculate by…

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Q: Write Z₁ and Z2 in polar form. Z1 = Z2 = Z₁ = 2√3-21, Z₂ = −1 + i Find the product Z₁²₂ and the…

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Q: 3. (a) Find the Laplace transform of (i) f(t)=17te-2-3 sin(9t) (ii) fo

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: (5+51)³

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Q: Question Let h(x) = f(x)g(x). If ƒ(−6) = 4, ƒ' (−6) = −2, g(−6) = 2, and g'(-6) = 5, what is h'(-6)?…

A: Use product rule of differentiation.

Q: Factor the polynomial and use the factored form to find the real zeros. (Enter your answers as a…

A: Here we have given a polynomialp(x)=x4-3x2-4. Now let x2=t ⇒p(t)=t2-3t-4 Now using the Quadratic…

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Q: = 9,g(-1) = -7, and is h' (-1)?

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Q: (x - 1) If 1 / ² ) = = √ Ada² + √ dx [ B (x − 3)(x + 7) - 3 - then A+B = Bdx x +7'

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A: current output of the machine = 8525 unit per hour

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Q: [3] Find dy for the curve given by: 4x -x²y³ = e5y +9y

A: We can find the derivative by using the implicit differentiation.

Q: Suppose f(x, y) = √/tan(x) + y and u is the unit vector in the direction of (0,—3). The (a) Vƒ(x, y)…

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Q: 3.) Find y(4) if y=3x³ +2x² −x+9

A: Topic = Derivative

Q: Consider the following. y = x² y = 6-x 4 (a) Find the area of the region by integrating with respect…

A: Note: Since you have asked multiple questions we will solve the first question for you. To get the…

Q: - Let C be the curve defined by R(t) = (2e²t - 3,1 - e²t, 2e²t). i. Find a vector equation of the…

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Q: 2. Define G(n) positive. -¹e dr. Show the reduction formula G(n + 1) = nG(n) if n is

A: Concept: Integration by parts: ∫f(x)g(x)=f(x)∫g(x)dx-∫ddxf(x)∫g(x)dxdx L hospital rule: A general…

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Q: rotate the point (2,8) by the (3/5,4/5) about the origin (0,0). (3/5,4/5) is on the unit circle.

A: Given data, Point A(2,8)

Q: Suppose a product's revenue function is given by R(q) - 4q² + 500g, where R(q) is in dollars and q…

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Q: Find fx(x,y) and fy(x,y). Then, find fx (2,- 4) and fy (-4,4). f(x,y) = 4x cos (лу) fx(x,y)= (Type…

A: Implicit differentiation is done and then values of x and y are substituted.

Q: Find the values of x, y and z that correspond to the critical point of the function: 2 = f(x, y) =…

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Q: Consider g(y)=y4/4+1/8y2. (a) Find the derivative. (b) Find the expression for 1+[g′(y)]2. (c)…

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Q: Continuing with the same table of values for f(t), is f'(t) increasing or decreasing? t f(t) 1 10 O…

A: From the given table we can see that, the value of function is increasing from t=1 to t=5. Then it…

Q: Exercise 7 y v = (3.x-2) 6: The Chain Rule (a) Decompose the function in the form y=f(u) and u= g(x)…

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Q: Using the same graph of f(x), what is lim f(x) ? X-2 1. ANL 0 2 3 2 -1- -2+ -2 doesn't exist -1

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Q: Q3 Calculate the area of the shaded region in the given figure y Focus point Parabola curve P- 2p 8p…

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Q: Implicit Differentiation using f, fy & f Let 20x² 1 dy dr dy Use partial derivatives to calculate at…

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Q: Given the function below 3 25 g(x) = X x+1 Which of the following leads to the solution of the…

A: Topic = Function

Q: | r - 1 dr

A: To evaluate the given integral.

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Q: Determine R³(t) if R²' (t) = <2e²+-41, +/= 1+1) and R (2) = <3, -5,0).

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Q: Assume that f (x) and g(x) are both differentiable functions for all x. Find the derivative of h(x)…

A: Given h(x)=f(x)·g(x)2

Q: Find the linearization. L(x) of f(x)=x² +1/x a+x= 1₁

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Q: while

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Q: Suppose that a population develops according to the logistic equation dP dt = 0.06P − 0.0006P2,…

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