Show that the function f(x) = e1/2[(x-p)/a}° has inflection points at x = u ±o.

Q: E Find the derivatives of y with respect to x: a) y = xex - ex b) y = e(4x+;) c) y = e*(sin x + cos…

A: we have to find the derivative of following function with respect to y (a) given y=xex-ex…

Q: Determine the numerical value of dF of the function F(x, y) = e-3y cos(nx) given that X = 1, y =…

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Q: al derivatives of t 'sin(z+y)

A: According to our terms and condition i have solved first question for next question repost

Q: Find the value of dz and dz/ dy at the point A when x changes by (0.01) and y changes by (- 0.01) xe…

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Q: and Suppose z is a function of a and y, and tan Vy2 + x² = z*e6y. Solve for dx dy

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Q: Q.2 Evaluate I = f* x*(1 - √x) dx using Beta-Gamma functions.

A: Given: Integral I = ∫01x4(1-x)5dx We have to evaluate the given integral using Beta Gamma function.

Q: Find the derivatives of y with respect to x: a) y = xe* - e* b)' y = e(4x+) e(tx+) X. c) y = e*(sin…

A: Since you have posted multipart question and we can answer three subparts. So, answered first three…

Q: Given f(z) = | t2 – 16 dt 1+ cos²(t) OS At what value of a does the local max of f(x) occur?

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Q: Find the particular antiderivative of the function f(x) point (0, –1). e" (2ª – 1) whose graph…

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Q: The linear approximation at x = 0 to sin(9x) is A + Bx where A is: and where B is:

A: Given fx=sin9x Differentiate fx=sin9x with respect to x, we get f'x=ddxsin9x=9cos9x Hence,…

Q: Let y=e^(x/2).Find the differential dy when x=1 and dx=0.3 Find the differential dy when x=1 and…

A: Given function is The differential dy is evaluated as follows,

Q: Find the derivative of y with respect to t at t=2 if a) у %3D х + sinх - cos(1 + x+x?) аnd x = (t/t…

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Q: Find the most general antiderivative of the function. f(x) = + 3 cos x

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Q: dw H.W: Use the chain rule to find the derivative dt with x = cos x = cos² t, y = sin² == and…

A: Given :w=xz+yzx=cos2t    and y=sin2t   z=1t

Q: 1. Find the derivatives of the given functions. a. y= arccos(x b. y = In (arctan x) c. y= csc (2u+1)…

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Q: (1) (a) Find the derivatives of functions f(x) = e2 and g(x) = 5æ?. (b) Compute the definite…

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Q: 1. If F(x)= = cos a sin r (√t-1)' dt, find F'(x).

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Q: 2. Find the derivative (dy/dx) of the following functions: h) y = 3x7 - 7x3 + 21x2 i) y = (x2 +…

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Q: B. Find y). 1. y = cosh?x 2. y = x tan-1 x - In vx2 + 1

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Q: Find the linear approximation of the function at the given point: f(x, y) = 2 sin x – 3 cos y at (0,…

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Q: Where is the function f(x, y) = e' arctan (VI+In(x+y)

A: In this question, the concept of continuity is applied. Given function is fx,y=etan-11+lnx+y

Q: Find the antiderivative of f(x)=cos(3x)

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Q: of

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Q: Let y = e/3 Find the differential dy when x = 5 and dx 0.2 Find the differential dy when x 5 and dx…

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Q: /4 Find the derivative of y with respect to t. (a) y = In(3te-1) (b) y = esin t (In t² + 1) (c) y =…

A: Given functions,  (a)  y=ln3te-1 (b)  y=esintlnt2+1 (c)  y=tlog3e(sint)(ln3) The objective is to…

Q: The tangent line to the curve y=f(x) is horizontal at where X = Xo f f(xx) = 00 A O f(xo) = 00 .8 O…

A: The tangent line to the curve y=f(x) is horizontal at where x=x0 if

Q: Find the general antiderivative of the given function. f(x)= sin (7y)+ cos (3y)

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Q: Find the value of dz and dz/ dy at the point A when x changes by (0.01) and y changes by (-0.01) xe…

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Q: Let h(x) = e*. f(x) and assume that f(ln 4) = -5 and f'(ln 4) = 6. Find the equation of the line…

A: We have to find equation of the line tangent to y=hx when x=ln(4)

Q: Assuming 9x° – 5y - 4xy = 0 defines y as a differentiable function of x, use the theorem dx - to…

A: Given: 9x3-5y2-4xy=0 We have to calculate dydx(1,1) by the given formula.

Q: Find the linear approximation at x = 0 to each of f(x) (x + 1)?, g(x) = 1+ sin(2x) and h(x)= e2*.…

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Q: 4. Find the indicated higher-order derivative of the given functions. d'y а. у %3D 8е* + sin x; dx7…

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Q: 1. Determine the equation of the tangent line to the graph of f(a) = [² pr+sin r = x = 0. cos (t² +…

A: Above equation of tangent is given.

Q: The derivative of y with respect to a given ¹ = 1 is Oy' = yx²-¹ O y'= 0 Onone of the choices Oy' =…

A: I have stated the used formula in the solution.

Q: Find In(y') at the point (0, 1/e) where xy° – In(xª + y) = 1.

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Q: Evaluate the derivative of e22.1.png acos(b/x) COS f(x) = x2 if a = 71 and b = 0.5 at x = 2 using…

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Q: 2. Show that the function u = p(xy) + Vxy v(y/x) provides the equation = 0. dy? -

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Q: Find the particular antiderivative of the function f(x) = e"(2" – 1) whose graph passes through the…

A: Integration

Q: Determine the numerical value of dF of the function F(x, y) = e-3y cos(nx) given that X = 1, y =…

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Q: The linear approximation at x = 0 to sin(4x) is A + Bx where A is: and where B is:

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Q: Suppose g(x) = = A, and f' (1) = B. Find the derivative In(In(In(f(x)))), %3D f(1) = dg dx \x=1…

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Q: Consider the function g(x) = 5 S cos t dt – x?. Then g' (x) is

A: Given gx=12∫x4x2costdt  -x2

Q: Find the antiderivative of the function f(x) = - 4 sin (4x) when C = 0. The antiderivative is

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Q: xy = In (2y) – e

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Q: 3. Find the derivatives of y with respect to x: a) y = xe* – e* b)' y = e(4x+±) c) y = e (sin x +…

A: To find- Find the derivatives of y with respect to x: y = xex - ex y = e4x + 1x y = exsinx + cosx y…

Q: Find the value(s) of @ for which y = cos ot satisfies d'y + 16y = 0. di? Enter your answers in…

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Q: Use the appropriate form of the chain rule to find the derivatives. W = 5x2 + 5y? + z²; x = p sin o…

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Q: The linear approximation at x = 0 to sin(7x) is A + Bx where A is: and where B is:

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Q: implicitly dx

A: Solved below

Q: 18. The equation of the tangent line to 2² sin T # 0 f(x) = 0 x = 0 at r = 0 is 1 (a) y = -x (b) y =…

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